Question

Suppose that 73.2% of all adults with type 2 diabetes also suffer from hypertension. After developing a new drug to treat type 2 diabetes, a team of researchers at a pharmaceutical company wanted to know if their drug had any impact on the incidence of hypertension for diabetics who took their drug. The researchers selected a random sample of 1000 participants who had been taking their drug as part of a recent large-scale clinical trial and found that 718 suffered from hypertension.

The researchers want to use a one‑sample ?z‑test for a population proportion to see if the proportion of type 2 diabetics who have hypertension while taking their new drug, ?p, is different from the proportion of all type 2 diabetics who have hypertension. They decide to use a significance level of ?=0.01α=0.01.

Determine the ?-valueP-value for this test. Give your answer precise to three decimal places.

Determine the value of the ?z‑test statistic. Give your answer precise to two decimal places.

Determine if the requirements for a one‑sample ?z‑test for a proportion been met. If the requirements have not been met, leave the rest of the questions blank.

The requirements have been met because the sample was appropriately selected, the variable of interest is categorical with two possible outcomes, and the sampling distribution is approximately normal.

The requirements have not been met because there are two samples: the type 2 diabetics with hypertension who are not taking the drug and the ones who are taking the drug.

The requirements have been met because the sample was appropriately selected, the variable of interest is categorical with two possible outcomes, and the sample size is at least 30.

The requirements have not been met because the population standard deviation is unknown.

Select the correct null (?0H0) and alternative (?1H1) hypotheses for this test.

?0:?=0.732H0:p=0.732 and ?1:?≠0.732H1:p≠0.732

?0:?=0.732H0:p=0.732 and ?1:?<0.732H1:p<0.732

?0:?=0.732H0:p=0.732 and ?1:?̂ ≠0.718H1:p^≠0.718

?0:?̂ =0.732H0:p^=0.732 and ?1:?̂ ≠0.732H1:p^≠0.732

?0:?̂ =0.718H0:p^=0.718 and ?1:?̂ ≠0.718H1:p^≠0.718

?=z=

?-value=P-value=

Select the correct decision and conclusion.

The researchers should not reject the null hypothesis. There is insufficient evidence (?>0.01P>0.01) that the proportion of type 2 diabetics taking the drug that have hypertension is different from 0.732.

The researchers should not reject the null hypothesis. There is sufficient evidence (?<0.01P<0.01) that the proportion of type 2 diabetics taking the drug that have hypertension is different from 0.732.

The researchers should reject the null hypothesis. There is insufficient evidence (?>0.01P>0.01) that the proportion type 2 diabetics taking the drug that have hypertension is different from 0.732.

The researchers should reject the null hypothesis. There is sufficient evidence (?<0.01P<0.01) that the proportion of type 2 diabetics taking the drug that have hypertension is different from 0.732.

Answer 1

The requirements have been met because the sample was appropriately selected, the variable of interest is categorical with two possible outcomes, and the sampling distribution is approximately normal.

The researchers should not reject the null hypothesis. There is insufficient evidence (P>0.01) that the proportion of type 2 diabetics taking the drug that have hypertension is different from 0.732.