A simple random sample of the sitting heights of 36 male students has a mean of 92.8 cm. The population of males has sitting heights with a mean of 91.4 cm and a standard deviation of 3.6 cm. Using a 0.05 significance level to test the claim, the P-value of 0.0198 is found. What is the final conclusion about testing the claim that male students have a sitting height different from 91.4 cm?

Question

A) There is not sufficient evidence to support the claim that male students have a sitting height different from 91.4 cm. 0
B) There is sufficient evidence to support the claim that male students have a sitting height different from 91.4 cm.
C) There is sufficient evidence to support the claim that male students have a sitting height the same as 91.4 cm.
D) There is not sufficient evidence to support the claim that male students have a sitting height the same as 91.4 cm.

Answer 1

To determine the conclusion regarding the claim that male students have a sitting height different from 91.4 cm, we need to analyze the given P-value in relation to the significance level of 0.05.

Since the significance level (α) is 0.05 and the P-value found is 0.0198, we compare:

• P-value = 0.0198
• Significance level (α) = 0.05

Given that the P-value (0.0198) is less than the significance level (0.05), we reject the null hypothesis. The null hypothesis in this context is that the mean sitting height of male students is equal to 91.4 cm, while the alternative hypothesis is that it is different from 91.4 cm.

Because we reject the null hypothesis, we conclude that there is sufficient evidence to support the claim that male students have a sitting height different from 91.4 cm.

Thus, the correct conclusion is:

B) There is sufficient evidence to support the claim that male students have a sitting height different from 91.4 cm.