Warm Up For a sample of size 23 with an area to the right=.05, what would the t value be? 90% confidence with n=24. What would the t value be? If df=19 and t=.90 and it’s a right tailed test, what would the p value be?

Ch. 23 – Inferences About Means (Day 2: Confidence Intervals & Hypothesis Tests) Part VI – Learning about the World

Conditions for Procedures Involving Sample Means To use the z-distribution Random sample n < 10%N Pop. approx. normal or n ≥ 30 To use the t-distributions Random sample n < 10%N Pop. approx. normal is still a condition, but it is not as strict for t (we will talk about this condition more tomorrow)

Using t for hypothesis testing… The average resting systolic blood pressure is 120 mm Hg. The director of the residency program at a medical school believes that the stress of the program causes higher blood pressure in the new residents. The director took a sample of 20 first year residents. He found that their mean systolic blood pressure was mm Hg, with a standard deviation of 9.96 mm Hg. Can the director conclude that the average blood pressure is higher for new residents?

ConditionCheck Random Sample Assume n < 10%NAssume 20 < 10% of all residents Pop approx. normal Assume (for now) Since p < α, reject H o. There is enough evidence to conclude that the average blood pressure for all new residents is more than 120 mmHg. p <.0005 μ = the mean systolic blood pressure for all first year residents H 0 : μ = 120 mmHg H a : μ > 120 mmHg One-sample t-test, α =.05, df = 19

Confidence Intervals In the previous problem, construct a 98% confidence interval for the mean blood pressure of first year residents. Statistic ± critical value · standard deviation ConditionCheck Random Sample Assume n < 10%NAssume 20 < 10% of all residents Pop approx. normal Assume (for now) 1-Sample t- interval, df = 19

Don’t forget to interpret… We are 98% confident that the true mean blood pressure for all first year residents in the program is between mmHg and mmHg.

Homework 23-2 p. 554 #14, 17, 30 Remember that if you have a df that is not on the table, use the next smallest one