Consider a test of [tex]H_0: \mu \geq 97[/tex] versus [tex]H_a: \mu < 97[/tex]. If the p-value was found to be 0.013, what would be the correct conclusion at an alpha = 0.05 significance level?

a) There is sufficient evidence that accepts the claim that the mean is 97.
b) There is sufficient evidence to reject the claim that the population mean is 97 and favor the alternative that the population mean is greater than 97.
c) There is sufficient evidence to reject the claim that the population mean is 97 and favor the alternative that the population mean is less than 97.
d) Insufficient evidence to make any conclusion. More data should be obtained.

Question

11-09-2023
Mathematics

High School

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Consider a test of [tex]H_0: \mu \geq 97[/tex] versus [tex]H_a: \mu < 97[/tex]. If the p-value was found to be 0.013, what would be the correct conclusion at an alpha = 0.05 significance level?

a) There is sufficient evidence that accepts the claim that the mean is 97.
b) There is sufficient evidence to reject the claim that the population mean is 97 and favor the alternative that the population mean is greater than 97.
c) There is sufficient evidence to reject the claim that the population mean is 97 and favor the alternative that the population mean is less than 97.
d) Insufficient evidence to make any conclusion. More data should be obtained.

Answer :

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monikasaxena8519 monikasaxena8519 · Answer 1 · 2024-05-21T04:37:22-04:00

The correct option is c) There is sufficient evidence to reject the claim that the population mean is 97 and favor the alternative that the population mean is less than 97.

Considering a test of H0: \\mu \\geq 97 versus Ha: \\mu < 97 and given that the p-value is 0.013, we compare it with alpha (\\u03b1) = 0.05 to determine our conclusion. Since the p-value of 0.013 is less than the significance level of 0.05, we reject the null hypothesis. Therefore, the correct option is c) There is sufficient evidence to reject the claim that the population mean is 97 and favor the alternative that the population mean is less than 97.