1. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2010 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Chapter 12 Additional Topics with Hypothesis Testing

2. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion Objectives: To conduct hypothesis tests for population proportions.

3. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion Definition: Rules for a testing a population proportion o If np  5, and o n(1 – p)  5, o then by the Central Limit Theorem, the test statistic is given by The test statistic, z, has a standard normal distribution.

4. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion Hypothesis Testing: A college is trying a new student registration system and would like to know if there is sufficient evidence to conclude that more than 60% of the students favor the new system. In a random sample of 520 students, 352 said that they prefer the new registration system. Conduct a hypothesis test at the 0.05 significance level. Solution: 1)H 0 : At most 60% of the students favor the new system. H a : More than 60% of the students favor the new system. 2)p = the true proportion of the student population who believe the new system is superior to the old system. 3)The key word here is “more.” Since the college is trying to determine if more than 60% of the students favor the new test, the test is one-sided.

5. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion Hypothesis Testing: A college is trying a new student registration system and would like to know if there is sufficient evidence to conclude that more than 60% of the students favor the new system. In a random sample of 520 students, 352 said that they prefer the new registration system. Conduct a hypothesis test at a 0.05 significance level. Solution: 4) H 0  : p  0.6 H a  : p  0.6 5)  0.05 6)Since np  5 and n(1 – p)  5, we can assume that the sampling distribution of is approximately normal, and therefore we can use the z-test. 7)Since  0.05 and the test is one-sided, z   z 0.05  1.645.

6. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion Hypothesis Testing: A college is trying a new student registration system and would like to know if there is sufficient evidence to conclude that more than 60% of the students favor the new system. In a random sample of 520 students, 352 said that they prefer the new registration system. Conduct a hypothesis test at a 0.05 significance level. Solution: 8) 9)Since 3.58  1.645  z , reject the null hypothesis. 10) There is sufficient evidence at the 0.05 significance level that more than 60% of the students prefer the new registration system.

7. HAWKES LEARNING SYSTEMS math courseware specialists If the null hypothesis is true, 95% of the time will be less than 1.645 standard deviations above the hypothesized value of p, which means the value of the z-test statistic will be less than 1.645. Hypothesis Testing: Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion

8. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: The rejection region can be graphed on the real number line, as follows. Then the test statistic can be compared against the rejection region on the real number line. Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion

9. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion Hypothesis Testing: The mayor of Savannah wants to know if the majority of the city’s residents are in favor of building a toll bridge across the Savannah River. A random sample of 420 residents is surveyed and 228 of them are in favor of the toll bridge. Conduct a hypothesis test at the 0.01 significance level to determine if a majority of the residents are in favor of the bridge. Solution: 1)H 0 : At most 50% of the residents favor the new toll bridge. H a : More than 50% of the residents favor the new toll bridge. 2)p = the true proportion of the residents who in favor of the bridge. 3)The key word here is “more.” Since the mayor wants to know if more than 50% of the residents favor the new bridge, this is a one- sided test.

10. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion Hypothesis Testing: Solution: 4)  H 0  : p  0.5 H a  : p  0.5 5)  0.01 6)Since np  5 and n(1 – p)  5 we can assume that the sampling distribution of is approximately normal, and therefore we can use the z-test. 7)Since  0.01 and the test is one-sided, z   z 0.01  2.33. The mayor of Savannah wants to know if the majority of the city’s residents are in favor of building a toll bridge across the Savannah River. A random sample of 420 residents is surveyed and 228 of them are in favor of the toll bridge. Conduct a hypothesis test at the 0.01 significance level to determine if a majority of the residents are in favor of the bridge.

11. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion Hypothesis Testing: Solution: 8) 9)Since 1.76  2.33  z , fail to reject the null hypothesis. 10) There is not sufficient evidence at the 0.01 significance level to conclude that the majority of residents are in favor of building the toll bridge. The mayor of Savannah wants to know if the majority of the city’s residents are in favor of building a toll bridge across the Savannah River. A random sample of 420 residents is surveyed and 228 of them are in favor of the toll bridge. Conduct a hypothesis test at the 0.01 significance level to determine if a majority of the residents are in favor of the bridge.

12. HAWKES LEARNING SYSTEMS math courseware specialists If the null hypothesis is true, 99% of the time will be less than 2.33 standard deviations above the hypothesized value of p, which means the value of the z-test statistic will be less than 2.33. Hypothesis Testing: Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion

13. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: The rejection region can be graphed on the real number line, as follows. Then the test statistic can be compared against the rejection region on the real number line. Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion

14. HAWKES LEARNING SYSTEMS math courseware specialists P-Values and Proportions: The rules for rejection of a null hypothesis using the P-value are the same as for population means. If the computed P-value is smaller than , reject the null hypothesis in favor of the alternative. If the computed P-value is greater than , fail to reject the null hypothesis. Additional Topics with Hypothesis Testing Section 12.1 Testing a Hypothesis About a Population Proportion

15. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.2 Testing a Hypothesis About a Population Variance Objectives: To conduct hypothesis tests for population standard deviations.

16. HAWKES LEARNING SYSTEMS math courseware specialists Definition: The appropriate test statistic for a hypothesis about a population variance is the chi-square test statistic given by where Note: The steps for testing a population variance are identical to those for testing population means and proportions. The chi- square test requires the assumption that the population is normally distributed. Additional Topics with Hypothesis Testing Section 12.2 Testing a Hypothesis About a Population Variance

17. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: A drug manufacturer believes that the manufacturing process is in control if the standard deviation of the dosage in each tablet is at most 0.10 milligrams. A sample of 30 pills is randomly selected and the sample standard deviation is found to be 0.14 milligrams. Conduct a hypothesis test at the 0.01 significance level to determine whether there is too much variation in the dosages. Assume that the dosages are normally distributed. Solution: 1)H 0 : The standard deviation is at most 0.10 milligrams. H a : The standard deviation is more than 0.10 milligrams. 2) n  30, the sample size s  0.14, the sample standard deviation  0  0.10, the acceptable population standard deviation 3)The key word here is “more.” Since the manufacturer needs to determine if the standard deviation is more than 0.10, the test is one-sided. Additional Topics with Hypothesis Testing Section 12.2 Testing a Hypothesis About a Population Variance

18. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: 4) H 0 :  0  0.10H a :  0  0.10 5)  0.01 6)Since we are concerned with population standard deviation, we will use the chi-square test statistic. 7)Since  0.01 and the test is one-sided, A drug manufacturer believes that the manufacturing process is in control if the standard deviation of the dosage in each tablet is at most 0.10 milligrams. A sample of 30 pills is randomly selected and the sample standard deviation is found to be 0.14 milligrams. Conduct a hypothesis test at the 0.01 significance level to determine whether there is too much variation in the dosages. Assume that the dosages are normally distributed. Solution: Additional Topics with Hypothesis Testing Section 12.2 Testing a Hypothesis About a Population Variance

19. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: 8) 9)Since reject the null hypothesis. 10) There is sufficient evidence at the 0.01 significance level that the standard deviation in the dosages is greater than 0.10 milligrams. A drug manufacturer believes that the manufacturing process is in control if the standard deviation of the dosage in each tablet is at most 0.10 milligrams. A sample of 30 pills is randomly selected and the sample standard deviation is found to be 0.14 milligrams. Conduct a hypothesis test at the 0.01 significance level to determine whether there is too much variation in the dosages. Assume that the dosages are normally distributed. Solution: Additional Topics with Hypothesis Testing Section 12.2 Testing a Hypothesis About a Population Variance

20. HAWKES LEARNING SYSTEMS math courseware specialists If the null hypothesis is true, 99% of the time the value of  2 with 29 degrees of freedom will be less than 49.588. Hypothesis Testing: Additional Topics with Hypothesis Testing Section 12.2 Testing a Hypothesis About a Population Variance

21. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: The rejection region can be graphed on the real number line, as follows. Then the test statistic can be compared against the rejection region on the real number line. Additional Topics with Hypothesis Testing Section 12.2 Testing a Hypothesis About a Population Variance

22. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means Objectives: To conduct a hypothesis test for two population means using large independent samples. To conduct a hypothesis test for two population means using small independent samples.

23. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means Definition: Rules for testing two population means o If n 1  30 and n 2  30, the sampling distribution of has an approximately normal distribution. o o If the two samples are independent, then by the Central Limit Theorem, the test statistic is given by where z has a standard normal distribution. and can be approximated with and respectively, if n 1  30 and n 2  30.

24. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means Definition: Rules for testing two population means o In previous hypothesis tests, the null and alternative hypotheses contained the hypothesized numeric value of the population parameter. o In hypothesis testing for two population means, you are testing that there is no difference in the means (the difference of the means equals zero) or, in other words, that the two means are equal. You will see the null hypothesis for a two-tailed test in two forms:  1  2  0, and  1  2.

25. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: An elementary school teacher is interested in knowing if there is sufficient evidence at the 0.05 level to conclude that there is a significant difference in the average reading speeds of fifth grade boys and fifth grade girls. She randomly selects 40 fifth grade boys and 40 fifth grade girls for the study. She gives each student several pages of the same book to read. The time it takes each student to complete the reading is recorded in minutes. The results are shown in the table. Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means Reading Speeds (in Minutes) ns Boys4010 3 Girls 4011 2

26. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: An elementary school teacher is interested in knowing if there is sufficient evidence at the 0.05 level to conclude that there is a significant difference in the average reading speeds of fifth grade boys and fifth grade girls. She randomly selects 40 fifth grade boys and 40 fifth grade girls for the study. She gives each student several pages of the same book to read. The time it takes each student to complete the reading is recorded in minutes. The results are shown in the table. Solution: 1)H 0 : There is no difference in the average reading speeds of fifth grade boys and fifth grade girls. H a : There is a difference in the average reading speeds of fifth grade boys and fifth grade girls. 2) Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means

27. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: Solution: 3)The key word here is “difference.” Since we are trying to establish a difference in means the test is two-tailed. 4)H 0 :  1  2  0H a :  1  2 ≠  0 5)   0.05 6)Since n 1  30 and n 2  30, we can assume that the sampling distribution of is approximately normally distributed and therefore we can use the z-test. Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means An elementary school teacher is interested in knowing if there is sufficient evidence at the 0.05 level to conclude that there is a significant difference in the average reading speeds of fifth grade boys and fifth grade girls. She randomly selects 40 fifth grade boys and 40 fifth grade girls for the study. She gives each student several pages of the same book to read. The time it takes each student to complete the reading is recorded in minutes. The results are shown in the table.

28. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: Solution: 7) Since  0.05 and the test is two-sided, z  /2  z 0.025  1.96. 8) 9) Since fail to reject the null hypothesis. 10) There is not significant evidence at the 0.05 level that the average reading speeds of fifth grade boys and girls are different. Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means An elementary school teacher is interested in knowing if there is sufficient evidence at the 0.05 level to conclude that there is a significant difference in the average reading speeds of fifth grade boys and fifth grade girls. She randomly selects 40 fifth grade boys and 40 fifth grade girls for the study. She gives each student several pages of the same book to read. The time it takes each student to complete the reading is recorded in minutes. The results are shown in the table.

29. HAWKES LEARNING SYSTEMS math courseware specialists If the null hypothesis is true, 95% of the time the value of the z-test statistic will be between  1.96 and 1.96. Hypothesis Testing: Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means

30. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: The rejection region can be graphed on the real number line, as follows. Then the test statistic can be compared against the rejection region on the real number line. Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means

31. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means Definition: Rules for testing two population means o If n 1 < 30 or n 2 < 30 and both populations of interest have approximately normal distributions, the sampling distribution of has a t-distribution. o o If both populations of interest have approximately equal (but unknown) variances, then the test statistic is given by If the null hypothesis is true, t has a t-distribution with n 1  n 2  2 degrees of freedom.

32. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: A cancer researcher believes that there may be an increase in life expectancy for women diagnosed with terminal breast cancer if they attend group therapy. 15 women attend therapy sessions and 15 do not attend therapy. The time from diagnosis until death is recorded. The average life expectancy is 3.8 years for the therapy group and 2.0 years for the other group. Their standard deviations are 0.6 years and 0.5 years, respectively. Conduct a hypothesis test at the 0.05 level to determine if there is an increase in life expectancy. Solution: 1)H 0 : The life expectancy of women who attend therapy is less than or equal to the life expectancy of those who do not attend. H a : The life expectancy of women who attend therapy is greater than the life expectancy of those who do not attend. 2) Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means

33. HAWKES LEARNING SYSTEMS math courseware specialists 3)The key word here is “increase.” Since we are trying to establish that one mean is greater than the other, the test is one-sided. 4)H 0 :  1  2  0H a :  1  2  0 5)   0.05 6) Since n 1 < 30 and n 2 < 30, we will use the t-test. We assume that the life expectancies for women with terminal breast cancer are normally distributed and the variances are approximately equal for patients who attend group therapy and those who do not. Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means Hypothesis Testing: A cancer researcher believes that there may be an increase in life expectancy for women diagnosed with terminal breast cancer if they attend group therapy. 15 women attend therapy sessions and 15 do not attend therapy. The time from diagnosis until death is recorded. The average life expectancy is 3.8 years for the therapy group and 2.0 years for the other group. Their standard deviations are 0.6 years and 0.5 years, respectively. Conduct a hypothesis test at the 0.05 level to determine if there is an increase in life expectancy. Solution:

34. HAWKES LEARNING SYSTEMS math courseware specialists 7)Since  0.05 and the test is one-sided, 8) Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means Hypothesis Testing: A cancer researcher believes that there may be an increase in life expectancy for women diagnosed with terminal breast cancer if they attend group therapy. 15 women attend therapy sessions and 15 do not attend therapy. The time from diagnosis until death is recorded. The average life expectancy is 3.8 years for the therapy group and 2.0 years for the other group. Their standard deviations are 0.6 years and 0.5 years, respectively. Conduct a hypothesis test at the 0.05 level to determine if there is an increase in life expectancy. Solution:

35. HAWKES LEARNING SYSTEMS math courseware specialists 9)Since reject the null hypothesis. 10) There is sufficient evidence at the 0.05 level that the average life expectancy from diagnosis until death for women with terminal breast cancer is significantly longer for those who attend group therapy than for those who do not. Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means Hypothesis Testing: A cancer researcher believes that there may be an increase in life expectancy for women diagnosed with terminal breast cancer if they attend group therapy. 15 women attend therapy sessions and 15 do not attend therapy. The time from diagnosis until death is recorded. The average life expectancy is 3.8 years for the therapy group and 2.0 years for the other group. Their standard deviations are 0.6 years and 0.5 years, respectively. Conduct a hypothesis test at the 0.05 level to determine if there is an increase in life expectancy. Solution:

36. HAWKES LEARNING SYSTEMS math courseware specialists If the null hypothesis is true, 95% of the time the value of the t-test statistic will be less than 1.701. Hypothesis Testing: Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means

37. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: The rejection region can be graphed on the real number line, as follows. Then the test statistic can be compared against the rejection region on the real number line. Additional Topics with Hypothesis Testing Section 12.3 Comparing Two Population Means

38. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.4 Paired Difference Objectives: To conduct a hypothesis test concerning the difference between two population means using dependent samples.

39. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.4 Paired Difference Dependent – if the two data sets are connected. Also referred to as matched pairs or paired data. Paired Difference – the difference between each pair of values in the data set, D  x 2 – x 1. Definitions: If subtracting the before treatment value from the after treatment value, a reduction in the value would be a negative number. The inequality signs will also be reversed: a “reduction of more than” would be.

40. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.4 Paired Difference Test Statistic for Dependent Samples: When calculating the sample mean of the paired differences, round to one more decimal place than given in the original data. If the differences are normally distributed and the null hypothesis is true, the test statistic has a t-distribution with n D – 1 degrees of freedom.

41. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.4 Paired Difference Hypothesis Testing: A researcher is interested in knowing the effect which one ounce of 100-proof alcohol has on people’s reaction times. The researcher randomly selected 10 subjects and recorded their reaction times before and after drinking the alcohol. Conduct a hypothesis test at the 0.01 level to determine if the average reaction time is longer after drinking the alcohol. The reaction times are recorded below. Reaction Times (in Seconds) SubjectBeforeAfterDifference 10.40.5–0.1 20.5 0.0 30.60.7–0.1 40.40.6–0.2 50.50.6–0.1 60.4 0.0 70.40.5–0.1 80.50.7–0.2 90.60.8–0.2 100.40.5–0.1

42. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.4 Paired Difference Hypothesis Testing: A researcher is interested in knowing the effect which one ounce of 100-proof alcohol has on people’s reaction times. The researcher randomly selected 10 subjects and recorded their reaction times before and after drinking the alcohol. Conduct a hypothesis test at the 0.01 level to determine if the average reaction time is longer after drinking the alcohol. Solution: 1)H 0 : There is no difference in average reaction time before and after drinking one ounce of 100-proof alcohol. H a : The average reaction time is significantly longer after drinking one ounce of 100-proof alcohol. 2)  D  the population mean of the paired differences in reaction times 3)The key word here is “longer.” Since the researcher is testing that the reaction time is longer the test is one-sided.

43. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.4 Paired Difference 4)H 0 :  D  0H a :  D  0 5)  0.01 6)Since n D  30 will use the t-test. The differences are assumed to be normally distributed. 7)Since  0.01 and the test is one-sided, Hypothesis Testing: A researcher is interested in knowing the effect which one ounce of 100-proof alcohol has on people’s reaction times. The researcher randomly selected 10 subjects and recorded their reaction times before and after drinking the alcohol. Conduct a hypothesis test at the 0.01 level to determine if the average reaction time is longer after drinking the alcohol. Solution:

44. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.4 Paired Difference Hypothesis Testing: A researcher is interested in knowing the effect which one ounce of 100-proof alcohol has on people’s reaction times. The researcher randomly selected 10 subjects and recorded their reaction times before and after drinking the alcohol. Conduct a hypothesis test at the 0.01 level to determine if the average reaction time is longer after drinking the alcohol. Solution: 8) 9) Since reject the null hypothesis. 10) There is significant evidence at the 0.01 level that the average reaction time is higher after drinking one ounce of 100-proof alcohol.

45. HAWKES LEARNING SYSTEMS math courseware specialists If the null hypothesis is true, 99% of the time the value of the t-test statistic will be greater than  2.821. Hypothesis Testing: Additional Topics with Hypothesis Testing Section 12.4 Paired Difference

46. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: The rejection region can be graphed on the real number line, as follows. Then the test statistic can be compared against the rejection region on the real number line. Additional Topics with Hypothesis Testing Section 12.4 Paired Difference

47. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.5 Comparing Two Population Proportions Objectives: To conduct a hypothesis test for two population proportions from large independent samples.

48. HAWKES LEARNING SYSTEMS math courseware specialists Definition: Rules for testing two population proportions o If, the sampling distribution of has an approximately normal distribution. o The test statistic is given by and z has a standard normal distribution. Additional Topics with Hypothesis Testing Section 12.5 Comparing Two Population Proportions

49. HAWKES LEARNING SYSTEMS math courseware specialists Definition: Additional Topics with Hypothesis Testing Section 12.5 Comparing Two Population Proportions Rules for testing two population proportions o In previous hypothesis tests, the null and alternative hypotheses contained the hypothesized numeric value of the population parameter. o In hypothesis testing for two population proportions, you are testing that there is no difference in the proportions (the difference of the proportions equals zero) or, in other words, that the two proportions are equal. You will see the null hypothesis for a two-tailed test in two forms: p 1  p 2  0, and p 1  p 2.

50. HAWKES LEARNING SYSTEMS math courseware specialists Defective Phones # sampled# defective Plant A2005 Plant B20012 Additional Topics with Hypothesis Testing Section 12.5 Comparing Two Population Proportions Hypothesis Testing: An executive at a cell phone company has been bombarded with complaints about a new model of cell phone. Two plants produce the cell phone and he suspects that one of them is producing the defective phones. To test this theory he randomly selects 200 phones from each of the plants and counts the number of defective phones. Test the theory that there is a difference in the proportions of defective phones produced by the two plants at the 0.10 significance level.

51. HAWKES LEARNING SYSTEMS math courseware specialists Additional Topics with Hypothesis Testing Section 12.5 Comparing Two Population Proportions 1)H 0 : There is no difference in the proportions of defective phones produced at Plant A and Plant B. H a : There is a difference in the proportions of defective phones produced at Plant A and Plant B. 2) 3)The key word here is “difference.” Since the executive is testing whether there is a difference, the test is two-sided. Hypothesis Testing: Solution: An executive at a cell phone company has been bombarded with complaints about a new model of cell phone. Two plants produce the cell phone and he suspects that one of them is producing the defective phones. To test this theory he randomly selects 200 phones from each of the plants and counts the number of defective phones. Test the theory that there is a difference in the proportions of defective phones produced by the two plants at the 0.10 significance level.

52. HAWKES LEARNING SYSTEMS math courseware specialists 4)H 0 : p 1  p 2 H a : p 1 ≠  p 2 5)   0.10 6)The appropriate test statistic is z. 7)Since   0.10 and the test is two-sided, z  2  z 0.05  1.645. Additional Topics with Hypothesis Testing Section 12.5 Comparing Two Population Proportions Hypothesis Testing: Solution: An executive at a cell phone company has been bombarded with complaints about a new model of cell phone. Two plants produce the cell phone and he suspects that one of them is producing the defective phones. To test this theory he randomly selects 200 phones from each of the plants and counts the number of defective phones. Test the theory that there is a difference in the proportions of defective phones produced by the two plants at the 0.10 significance level.

53. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: Solution: 8) 9) Since reject the null hypothesis. 10) There is sufficient evidence at   0.10 to conclude that there is a difference in the proportions of defective cell phones produced by the two plants. Additional Topics with Hypothesis Testing Section 12.5 Comparing Two Population Proportions An executive at a cell phone company has been bombarded with complaints about a new model of cell phone. Two plants produce the cell phone and he suspects that one of them is producing the defective phones. To test this theory he randomly selects 200 phones from each of the plants and counts the number of defective phones. Test the theory that there is a difference in the proportions of defective phones produced by the two plants at the 0.10 significance level.

54. HAWKES LEARNING SYSTEMS math courseware specialists If the null hypothesis is true, 90% of the time the value of the z-test statistic will be between  1.645 and 1.645. Hypothesis Testing: Additional Topics with Hypothesis Testing Section 12.5 Comparing Two Population Proportions

55. HAWKES LEARNING SYSTEMS math courseware specialists Hypothesis Testing: The rejection regions can be graphed on the real number line, as follows. Then the test statistic can be compared against the rejection regions on the real number line. Additional Topics with Hypothesis Testing Section 12.5 Comparing Two Population Proportions