Significance Tests and Confidence Intervals assignment

A test of the hypotheses H0: = 7.5 versus Ha: < 7.5 has a probability of making a Type II error of 0.15. What is the power of this test?

0.85

On average, adults spend approximately 5 hours per night in NREM (non-rapid eye movement) sleep. A sleep study selects a random sample of adults and gives them each a weighted blanket. They would like to know if using the weighted blanket changes the mean number of hours per night of NREM sleep. We want to test = 5 versus ≠ 5 where = the true mean hours of NREM sleep per night for adults who use a weighted blanket. A 99% confidence interval for the true mean hours of NREM sleep per night for adults who use a weighted blanket is (5.1, 5.8) hours. Based on the confidence interval, what conclusion would you make for a test of these hypotheses?

does not 5 reject have is different from

The power of a test is the probability that the test will find convincing evidence for Ha when a specific alternative value of the parameter is true. Stated another way, power is equivalent to

rejecting H0 when you should reject H0.

A test of the hypotheses H0: = 7.5 versus Ha: < 7.5 has low power. What can the researcher do to increase the power of the test to reject the null hypothesis if = 7? Check all that apply.

The researcher can increase the sample size. The researcher can increase the significance level of the test. The researcher can try to decrease the probability of making a Type II error.

A sleep scientist wanted to determine if the amount of sleep that highly productive individuals tend to get differs from the recommended 7.5 hours of sleep per night, using = 0.05. = 7.5 versus ≠ 7.5 where = the true mean amount of sleep per night for highly productive individuals Rather than test these hypotheses, she computes a 95% confidence interval for the true mean amount of sleep per night for highly productive individuals. The 95% confidence interval is (5.8, 6.4). Based upon the confidence interval, can the sleep scientist reject the null hypothesis?

A. She can reject the null hypothesis at = 0.05 because 7.5 is not contained in the 95% confidence interval.

A sleep scientist wanted to determine if highly productive individuals tend to get less than the recommended 7.5 hours of sleep per night, using = 0.05. She wants to test the hypotheses = 7.5 versus < 7.5 where = the true mean amount of sleep per day for highly productive individuals. She selects a random sample of 30 highly productive individuals and calculates the mean and standard deviation of the number of hours of sleep they get per night. The power of this test to reject 7.5 hours, if the true mean of = 7, is 0.65. Select all options that would have increased the power of this test:

Use n = 40 instead of n = 30. Use = 0.10 instead of = 0.05. Attempt to detect = 6.5 instead of = 7.

An article claims that babies spend twice as much time in REM (rapid eye movement) sleep than adults. This implies that babies have an average of 6 hours of REM sleep per night. A doctor would like to test the hypotheses = 6 versus ≠ 6 where = the true mean amount of REM sleep per night for babies. A 95% confidence interval for the true mean amount of REM sleep per night for babies is (5.45, 6.25) hours. Based on the confidence interval, what conclusion would you make for a test of these hypotheses?

does 6 fail to reject do not have is different from

A sleep scientist wanted to determine if highly productive individuals tend to get less than the recommended 7.5 hours of sleep per night, using = 0.05. She wants to test the hypothesesH0: = 7.5 versus Ha: < 7.5 where = the true mean amount of sleep per day for highly productive individuals. She selects a random sample of 30 highly productive individuals and calculates the mean and standard deviation of the number of hours of sleep they get per night. The power of this test to reject 7.5 hours, if the true mean is , is 0.57.

mean 7 the alternative hypothesis

When a test is one-sided✔ two-sided: If the value of interest falls outside a 95% confidence interval, we will reject the null hypothesis at the = X 0.01✔ 0.050.10 significance level. If the value of interest falls outside a 99% confidence interval, we will reject the null hypothesis at the = ✔ 0.010.050.10 significance level.

one-sided 0.05 0.01