Question

Consider the following hypothesis test:

H0: ? = 100

HA: ? ? 100

A sample of 65 is used. Identify the p-value and state your conclusion for each of the

following sample results. Use ? = 0.05. (Note: Approximate p-values are sufficient.)

a) x = 103 and s = 11.5

b) x = 96.5 and s = 11.0

c) x = 102 and s = 10.5

Answer 1

For each sample result, the test statistic and p-value are calculated to make a conclusion for the hypothesis test. In all three cases, the p-value is greater than the significance level α = 0.05, so we fail to reject the null hypothesis H0.

Step-by-step explanation:

To find the p-value and state the conclusion for each sample result, we will:

1. Calculate the test statistic using the formula: z = (x - μ) / (s / √n)
2. Find the area to the right of the test statistic using a standard normal distribution table
3. Compare the p-value to α = 0.05 to make a conclusion

a) For x = 103 and s = 11.5:

Test statistic: z = (103 - 100) / (11.5 / √65) ≈ 1.33

Area to the right of z = 1.33 is approximately 0.0912 (from the table)

p-value = 0.0912 > α = 0.05

Conclusion: Fail to reject the null hypothesis H0

b) For x = 96.5 and s = 11.0:

Test statistic: z = (96.5 - 100) / (11.0 / √65) ≈ -1.39

Area to the right of z = -1.39 is approximately 0.9171 (from the table)

p-value = 0.9171 > α = 0.05

Conclusion: Fail to reject the null hypothesis H0

c) For x = 102 and s = 10.5:

Test statistic: z = (102 - 100) / (10.5 / √65) ≈ 0.95

Area to the right of z = 0.95 is approximately 0.1711 (from the table)

p-value = 0.1711 > α = 0.05

Conclusion: Fail to reject the null hypothesis H0