Homework: pg. 709 #27, 29 27.) µ=the mean dissolved oxygen content in the stream. Ho:µ=5 Ha:µ<5 Conditions: states random, sample size is large so Normal.

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Homework: pg. 709 #27, 29 27.) µ=the mean dissolved oxygen content in the stream. Ho:µ=5 Ha:µ<5 Conditions: states random, sample size is large so Normal by CLT, population of possible samples is larger than 450. Z=-2.77, P-value=0.0028, need sketch! We reject the null. If the population mean were 5, then the probability of getting a sample mean of 4.62 is .28%. We have strong evidence that the mean dissolved oxygen content in the stream is less than 5 mg.

Homework: pg. 709 #27, 29 29.) A.) The graph looks roughly symmetric so it is possible for it to be Normal. µ=the mean target value of tablet hardness Ho:µ=11.5 Ha:µ≠11.5 Conditions: assume SRS, see part A for Normality, population of tablets is larger than 200. Z=0.37, P-value=.7114, need sketch! We fail to reject the null. If the population mean were 11.5, then the probability of getting a sample mean of 11.516 is 71%. We do not have any evidence that the mean target level is not 11.5.

Confidence Intervals and Two-Sided Tests Section 11.2 Day 2

What are the two possible conclusions for a significance test?

What does it mean to “reject the null?”

Two-Sided Test- 5% Level Where is the “rejection line?” How many standard deviations away from the mean is the “rejection line?” µ Reject Fail to reject Reject µ

Confidence Interval-95% Notice z* is the same as the standard deviations away from the mean in the two-sided test Not reasonable µ not Reasonable reasonable

Together- Two-sided tests and confidence intervals µ *If your null hypothesis is in your confidence interval, then it is a reasonable guess….fail to reject. *If your null hypothesis is NOT in your confidence interval, then it is not a reasonable guess….REJECT the null.

Examples: pg. 712 #31, 32

Pg. 713 #35,37,38 Homework

Homework: pg. 713 #35, 37, 38 35.) A.) The sample is not an SRS so may not be representative of the population, Normality is reasonable due to large sample size. Independence is met because the population of pregnant women in Guatemala is more than 1600. B.) Ho:µ=9.5, Ha:µ≠9.5; z=2.21; P-value=0.0272; We reject the null. If the mean were 9.5, the probability of getting a sample mean of 9.57 is 2.72%. The mean calcium level in healthy, pregnant Guatemalan women likely differs from 9.5. C.) (9.508, 9.632) We are 95% confident that the mean blood calcium for these women is between these two numbers.

37.) A. Yes. We would not reject the null so it’s reasonable so it would be in our confidence interval. No. We would reject the null at the 10% level so the null is not reasonable and won’t be in our confidence interval. 38.) A. No. 13 is in the 90% confidence interval so the null cannot be rejected. **B. No. The sample mean is less than one standard error away from the mean. Yes. 10 is not in the 90% confidence interval so the null can be rejected at the 10% level. **D. It depends on which side; µ<10, the answer is no. µ>10, the answer is yes.