the distribution of the heights of five - year - old children has a mean of 42.5 inches. a pediatrician…

the distribution of the heights of five - year - old children has a mean of 42.5 inches. a pediatrician believes the five - year - old children in a city are taller on average. the pediatrician selects a random sample of 30 five - year - old children and measures their heights. the mean height of the sample is 43.6 inches with a standard deviation of 3.6 inches. the pediatrician conducts a one - sample t - test for $mu$ and calculates a p - value of 0.052. at the $alpha = 0.01$ level, what is the correct conclusion for this test? the pediatrician should reject the null hypothesis since 0.052 > 0.01. there is convincing evidence that the mean height of five - year - old children in this city is greater than 42.5 inches. the pediatrician should accept the null hypothesis since 0.052 > 0.01. there is not convincing evidence that the mean height of five - year - old children in this city is greater than 42.5 inches. the pediatrician should fail to reject the null hypothesis since 0.052 > 0.01. there is convincing evidence that the mean height of five - year - old children in this city is greater than 42.5 inches. the pediatrician should fail to reject the null hypothesis since 0.052 > 0.01. there is not convincing evidence that the mean height of five - year - old children in this city is greater than 42.5 inches.

the distribution of the heights of five - year - old children has a mean of 42.5 inches. a pediatrician believes the five - year - old children in a city are taller on average. the pediatrician selects a random sample of 30 five - year - old children and measures their heights. the mean height of the sample is 43.6 inches with a standard deviation of 3.6 inches. the pediatrician conducts a one - sample t - test for $mu$ and calculates a p - value of 0.052. at the $alpha = 0.01$ level, what is the correct conclusion for this test? the pediatrician should reject the null hypothesis since 0.052 > 0.01. there is convincing evidence that the mean height of five - year - old children in this city is greater than 42.5 inches. the pediatrician should accept the null hypothesis since 0.052 > 0.01. there is not convincing evidence that the mean height of five - year - old children in this city is greater than 42.5 inches. the pediatrician should fail to reject the null hypothesis since 0.052 > 0.01. there is convincing evidence that the mean height of five - year - old children in this city is greater than 42.5 inches. the pediatrician should fail to reject the null hypothesis since 0.052 > 0.01. there is not convincing evidence that the mean height of five - year - old children in this city is greater than 42.5 inches.

Answer

Answer:

The pediatrician should fail to reject the null hypothesis since 0.052 > 0.01. There is not convincing evidence that the mean height of five - year - old children in this city is greater than 42.5 inches.

Explanation:

Step1: Recall hypothesis - testing rule

In hypothesis testing, if the P - value is greater than the significance level $\alpha$, we fail to reject the null hypothesis.

Step2: Compare P - value and $\alpha$

We are given that $\alpha=0.01$ and the P - value = 0.052. Since $0.052>0.01$.

Step3: Make a conclusion

We fail to reject the null hypothesis. This means there is not convincing evidence to support the claim that the mean height of five - year - old children in the city is greater than 42.5 inches.