Testing a Claim about a Population Proportion assignment

According to shopper data, 97% of households purchase toilet paper. An analyst believes this is too low. To investigate, the analyst selects a random sample of 500 households and finds that 98% of them purchase toilet paper. We found that we do not have convincing evidence at the α = 0.05 level to conclude that the true proportion of all households that purchase toilet paper differs from 0.97. It can be difficult to detect such a small difference, such as from 0.97 to 0.98, even if the difference exists. What can be done to increase the power of this test to reject 0.97 if 0.98 is true? Check all that apply.

increase a increase n

Adults tend to believe that a majority of teenagers sleep in on Saturdays, but maybe that is a misconception. A random sample of 120 teenagers showed that 48 slept in the previous Saturday. Use the computer output provided below to determine if there is convincing evidence at the α = 0.05 level that the true proportion of teenagers who slept in on the previous Saturday is less than 0.5. Use this computer output to answer the questions.

is less than reject have less than 0.5

According to shopper data, 97% of households purchase toilet paper. An analyst believes this is too low. To investigate, the analyst selects a random sample of 500 households and finds that 98% of them purchase toilet paper. Do these data provide convincing statistical evidence at the α = 0.05 level to conclude that the true proportion of all households that purchase toilet paper differs from 0.97? Plan: The analyst should carry out a z-test for one proportion. Determine if each condition is met or not met.

met met 1.31 0.19 fail to reject

According to a recent study, 15% of adults who take a certain medication experience side effects. To further investigate this finding, a researcher selects a separate random sample of 150 adults, of which 32 experience side effects. The researcher would like to determine if there is convincing statistical evidence that the true proportion of adults who would experience side effects from this medication is greater than 0.15 using a significance level of α = 0.05. Complete the "State" and "Plan" steps. Which statements are true? Check all that apply.

H0: p = 0.15 The random condition is met. The 10% condition is met. The large counts condition is met. The test is a z-test for one proportion.

According to shopper data, 97% of households purchase toilet paper. An analyst believes this is too low. To investigate, the analyst selects a random sample of 500 households and finds that 98% of them purchase toilet paper. We found that we do not have convincing evidence at the α = 0.05 level to conclude that the true proportion of all households that purchase toilet paper differs from 0.97. The power of this test to reject p = 0.97 if 0.98 is true is 0.21. If the analyst were to decrease the significance level of the test, how would the power be affected?

It would decrease.

Adults tend to believe that a majority of teenagers sleep in on Saturdays, but maybe that is a misconception. A random sample of 120 teenagers showed that 48 slept in the previous Saturday. Use the computer output provided below to determine if there is convincing evidence at the α = 0.05 level that the true proportion of teenagers who slept in on the previous Saturday is less than 0.5. Use this computer output to answer the questions. Based upon the 95% confidence interval, it is reasonable to claim that the true proportion of all teenagers who slept in on the previous Saturday is between which two values?

0.3124 and 0.4877

According to shopper data, 97% of households purchase toilet paper. An analyst believes this is too low. To investigate, the analyst selects a random sample of 500 households and finds that 98% of them purchase toilet paper. We found that we do not have convincing evidence at the α = 0.05 level to conclude that the true proportion of all households that purchase toilet paper differs from 0.97. The power of this test to reject p = 0.97 if 0.98 is true is 0.21. Interpret the power of this test.

0.97 0.21 0.97

According to shopper data, 97% of households purchase toilet paper. An analyst believes this is too low. To investigate, the analyst selects a random sample of 500 households and finds that 98% of them purchase toilet paper. Do these data provide convincing statistical evidence at the α = 0.05 level to conclude that the true proportion of all households that purchase toilet paper differs from 0.97? Complete the "State" step for this test.

0.97 is different from 0.97 households purchase toilet paper

According to a recent study, 15% of adults who take a certain medication experience side effects. To further investigate this finding, a researcher selects a separate random sample of 150 adults, of which 32 experience side effects. The researcher would like to determine if there is convincing statistical evidence that the true proportion of adults who would experience side effects from this medication is greater than 0.15 using a significance level of α = 0.05. Complete the "Do" and "Conclude" steps using the z-table. Which statements are true? Check all that apply.

The test statistic is z = 2.172. The P-value is 0.015. We reject H0.