Question

you can calculate the p-value for a chi-square test using technology. after calculating the standardized test statistic, use the cumulative distribution function (cdf) to calculate the area under the curve. use the p-value method to test the claim.

a school administrator claims that the standard deviation for eighth-grade students on a test is greater than 35 points. a random sample of 27 eighth-grade students has a standard deviation of 36.9 points. at α = 0.01, is there enough evidence to support the administrator’s claim?

...

identify the standardized test statistic.

χ² = 28.899 (round to three decimal places as needed.)

identify the p-value.

p = 0.3157 (round to four decimal places as needed.)

choose the correct conclusion below.

○ a. reject h₀. there is enough evidence at the 1% level of significance to support the administrator’s claim.
○ b. fail to reject h₀. there is not enough evidence at the 1% level of significance to support the administrator’s claim.
○ c. fail to reject h₀. there is enough evidence at the 1% level of significance to support the administrator’s claim.
○ d. reject h₀. there is not enough evidence at the 1% level of significance to support the administrator’s claim.

Explanation:

To determine the conclusion, we compare the P - value (\( P = 0.3157 \)) with the significance level \( \alpha=0.01 \). Since \( 0.3157>0.01 \), we fail to reject the null hypothesis \( H_0 \). Failing to reject \( H_0 \) means there is not enough evidence at the 1% significance level to support the administrator's claim that the standard deviation is greater than 35 points.

Answer:

B. Fail to reject \( H_0 \). There is not enough evidence at the 1% level of significance to support the administrator’s claim.