An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given set of hypotheses and T test statistic. (a) HA: μ > 0.5, n = 21, T = 2.485 p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005 Determine if the null hypothesis would be rejected at α = 0.01. reject H0 fail to reject H0 Changed: Your submitted answer was incorrect. Your current answer has not been submitted. (b) HA: μ < 3, n = 17, T = 0.5 p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005 Determine if the null hypothesis would be rejected at α = 0.01.

(a) The correct interval is, 0.010 < p-value < 0.025. Fail to reject H₀.

(b) The correct interval is, p-value > 0.100. Fail to reject H₀.

Step-by-step explanation:

(a)

The information provided is:

Hₐ: μ > 0.5, n = 21, t = 2.485

Compute the p-value as follows:

               

The correct interval is, 0.010 < p-value < 0.025.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.011 > α = 0.01

Fail to reject H₀.

(b)

The information provided is:

Hₐ: μ < 3, n = 17, t = 0.5

Compute the p-value as follows:

               

The correct interval is, p-value > 0.100.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.312 > α = 0.01

Fail to reject H₀.

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