Question

The National Health Statistics Reports described a study in which a sample of 33 one-year-old baby boys were weighed. Their mean weight was 25.4 pounds with standard deviation 5.3 pounds. A pediatrician claims that the mean weight of one-year-old boys is greater than 25 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the =α0.05 level of significance and the P-value method with the TI-84 Plus calculator.

1) State the appropriate null and alternate hypotheses. H0=, H1= This hypothesis test is a (left tailed, right tailed or two tailed) test

2) Compute the P-value. Round the answer to four decimal places.

3) Determine whether to reject H0 (reject or not reject)

4) There (is or is not) enough evidence to conclude that the mean weight is 25.4 lbs.

Answer 1

1)

Answer:

This is a right-tailed test

Explanation:

The null hypothesis is defined as the mean weight of one-year-old boys is 25 pounds and the alternative hypothesis tests the claim that the mean weight of one-year-old boys is greater than 25 pounds.

2)

Answer:

Explanation:

Since we are comparing one sample mean with the population mean and the population standard deviation is not known, the t-test is used to test the hypothesis

Test-statistic

The t statistic is obtained using the formula,

P-value

The p-value is obtained from t distribution table for t = 0.434 and degree of freedom = n - 1 = 33 - 1 = 32. (In excel use function =T.DIST.RT(0.4336,32))

3)

Answer:

Do not reject H0

Explanation:

Since the P-value is greater than the significance level = 0.05 at a 5% significance level, the null hypothesis is not rejected.

4)

Answer:

There is not enough evidence to conclude that the mean weight is 25.4 lbs.

Explanation:

Since the null hypothesis is failed to reject, we can not conclude that the mean weight of one-year-old boys is greater than 25 pounds.