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3. Try It! Calcium Intake pg 130 Daily intake of calcium (mg) for 38 women. Concerned mean calcium intake for population is not meeting RDA level of 1200 mg; i.e. popul mean is less than the 1200 mg level. Test using a 5% significance level. a. State the hypotheses: H 0 :H a :

4. Try It! Calcium Intake b. Interpret the Std. Error of the mean (SEM):

5. Try It! Calcium Intake c. Give the observed test statistic value: Interpret as a difference from hypothesized mean of 1200:

6. Try It! Calcium Intake d.Sketch picture of p-value as an area under a distribution. e.Give p-value and conclusion at 5% significance level. Get ready for a clicker question …

7. Clicker in your answer … A decision was just made regarding the average calcium intake for the population of all such women. What type of statistical error could have been made? A) A Type 1 error B) A Type 2 error C) No mistake, the researcher is very smart!

8. 13.5 Relationship between Tests and CIs pg 131 CI provides a range of plausible (reasonable) values for the parameter. Null hypothesis gives a null value for the parameter. If null value is one of the “reasonable” values found in the CI, the null hypothesis would not be rejected. If null value was not found in the CI of acceptable values for the parameter, then the null hypothesis would be rejected.

9. 13.5 Relationship between Tests and CIs pg 131 Notes: (1) H a should be two-sided. Sometimes can reason through decision for a one-sided test (pg 575-576). (2)Significance level coincide with confidence level (e.g.  = 0.05 with a 95% confidence level). Sometimes can reason through decision if these don’t exactly correspond. (3)Relationship holds exactly for tests about a popul mean or difference betw two popul means. In most cases, will hold for tests about a popul proportion or difference betw two popul proportions (read bottom pg 575).

10. Try It! Time Spent Watching TV pg 132 Study on amt time teenagers spend watching TV. 95% CI for mean amt of time (hours) 2.6 ± 2.1  (0.5 hours, 4.7 hours) Look at each set of hypotheses and determine whether you would reject H 0, fail to reject H 0, or you cannot tell.

11. 95% CI: (0.5 hours, 4.7 hours) (a) Test H 0 :  = 5 vs H a :  ≠ 5 at  = 0.05 (b)Test H 0 :  = 4 vs H a :  ≠ 4 at  = 0.05 Reject H 0 Fail to Reject H 0 Can’t Tell

12. 95% CI: (0.5 hours, 4.7 hours) (c) Test H 0 :  = 4 vs H a :  ≠ 4 at  = 0.01 (d)Test H 0 :  = 4 vs H a :  ≠ 4 at  = 0.10 Reject H 0 Fail to Reject H 0 Can’t Tell

13. Try It! MBA grads Salaries page 133 Parameter: population mean expected salary,  (in $). A random sample of 1000 students who finished their MBA this year (from 129 business schools) resulted in a 95% confidence interval for  of (83700, 84800). a.What is the value of the sample mean? (Include your units)

14. Try It! MBA grads Salaries A 95% confidence interval for  is ($83,700, $84,800). b.True or false? If repeated samples of 1000 such students were obtained, we would expect 95% of the resulting intervals to contain the population mean. TrueFalse There is a 95% probability that the population mean lies between $83,700 and $84,800. TrueFalse

15. Click in answer: 95% CI for m is (83700, 84800). Expected earnings for graduates in past was $76,100. Test following hypotheses at 10% significance level H 0 :  = 76100 versus H a :  ≠ 76100. Our decision would be: A) Fail to Reject H 0 B) Reject H 0 C) Cant’ Tell

16. d. QQ-plot is provided for checking assumption that the response is normally distributed. Plot shows some departure from a straight line with a positive slope. Is this cause for concern that inference based on our confidence interval and hypothesis test would not be valid?

17. Yellow Card on the Big 5 Parameters We have covered most of the top 3 columns