Comparing Two Means Two Proportions Two Means: Independent Samples Two Means: Dependent Samples

Hypothesis Test for 2 Proportions When we want to compare two proportions, we proceed similarly to a test for 1 Proportion. Requirements: n 1 p 1, n 2 p 2, n 1 q 1, n 2 q 2 > 5 TI 84: Use 2-PropZTest for a hypothesis test and 2-PropZInt for a confidence interval.

Interpreting the Confidence Level A 95% confidence level means that if many studies are conducted, then each would produce its own confidence interval. 95% of these confidence intervals will contain the true population difference between the two proportions and 5% will not.

Interpreting the Confidence Interval (Both Positive or Both Negative) If a 95% confidence interval is [ a,b ] with both positive (negative), then with 95% confidence it can be concluded that the first variable is between 100x a % and 100x b % more (less) likely to occur than the second variable.

Interpreting the Confidence Interval (Different Signs) If a 95% confidence interval is [ a, b ] with a < 0 < b then with 95% confidence then we do not know which proportion is higher. We often say that the results are within the margin of error.

Interpreting the Level of Significance If a hypothesis test results in H 0 rejected with a 5% level of significance, then if H 0 is true and if another study was conducted with the same sample size as the current study, then there is a 5% chance that the null hypothesis would be rejected even though the null hypothesis is true.

Interpreting the P-Value (1 Tailed) If a left tailed (right tailed) hypothesis test results in a p-value of 0.03 and a sample difference between proportions of 8%, for example, then if H 0 is true and if another study was conducted with the same sample size as the current study, then there is a 3% chance that the new study will result in the first proportion being at least 8% less (more) than the second proportion.

Interpreting the P-Value (2 Tailed) If a two tailed hypothesis test results in a p- value of 0.03 and a sample difference between proportions of 8%, for example, then if H 0 is true and if another study was conducted with the same sample size as the current study, then there is a 3% chance that the new study will result in either the first proportion being at least 8% less than the second proportion or the first proportion being at least 8% more than the second proportion.

Difference Between Proportions Are transfer students from community colleges more likely to major in the health sciences than students who go directly to a university from high school? 42 of the 200 community college transfer students surveyed had majors in the health sciences and 50 of the 300 direct students had majors in the health sciences. What can be concluded at the 0.05 level? Also find a 95% confidence interval for this difference. 2-PropZTest, 2-PropZInt

Difference Between Proportions Are Democrats less likely to own an American car than Republicans? Of the 150 Democrats surveyed, 65 of them owned an American car and of the 120 Republicans surveyed 70 owned an American car. What can be concluded at the 0.05 level? Also find a 95% confidence interval for this difference. 2-PropZTest, 2-PropZInt

Difference Between Means Is there a difference between the amount of studying for male and female students? The 45 male students in the survey averaged 8 hours of studying per week and had a standard deviation of 3 hours. The 38 female students averaged 8.4 hours per week and had a standard deviation of 2.5 hours. What can be concluded at the 0.1 level of significance? Also find a 90% confidence interval for this difference. 2-SampTTest, 2SampTInt

Difference Between Means Are tips better on Saturdays compared to Fridays? A waiter looked at 32 tips from Fridays and found the mean to be 18% and the standard deviation 2.5%. For the 35 Saturday tips the mean was 19% and the standard deviation was 3%. What can be concluded at the 0.05 level of significance? Also find a 95% confidence interval for this difference. 2-SampTTest, 2SampTInt

Dependent Samples Two samples are called dependent or paired if there is a pairing between corresponding data entries of the two samples. The variables must be quantitative and subtraction must make sense. Before and after studies Twin Studies Comparison of two locations at many different times

Dependent Samples A study was done to see if Kirkwood receives more snow on average than Heavenly. The snow amounts in inches received for 8 randomly selected storms was tabulated. What can be concluded at the 0.05 level of significance? Assume a normal distribution Kir Hea L1 – L2 STO> L3, TTest, TInterval

Dependent Samples Nine people were tested for memory recall before and after drinking a shot of whiskey. The table below shows the number of digits they could recall for this before and after study. Is there evidence at the 0.05 level that memory is reduced after drinking alcohol? Before After L1 – L2 STO> L3, TTest, TInterval