Assume that in a hypothesis test with null hypothesis $\mathrm { H } _ { 0 } : \mu = 14.0 \text { at } \alpha = 0.10$ , that a value of 11.0 for the sample mean results in the null hypothesis being accepted. That corresponds to a confidence interval
Result of
A) The 0.10% confidence interval for the mean contains the value 11.0
B) The 90% confidence interval for the mean contains the value 14.0
C) The 90% confidence interval for the mean does not contain the value 14.0
D)There is insufficient information as to if the 90% confidence interval for the mean does or does not contain the value 11.0

Question

Quizplus · Accepted Answer

If the null hypothesis is accepted at a level of significance of 0.10, it means that the sample mean of 11.0 is not significantly different from the hypothesized population mean of 14.0. This implies that a 90% confidence interval for the population mean should include the hypothesized value of 14.0, which is option B. Option A is incorrect because the confidence interval would not be centered around the sample mean of 11.0 in this case. Option C is incorrect because it suggests that the 90% confidence interval does not contain the hypothesized value of 14.0, which contradicts the acceptance of the null hypothesis. Option D is incorrect because the information given is sufficient to determine that the 90% confidence interval contains the value of 14.0, but does not provide information about whether it contains the value of 11.0.

Assume That in a Hypothesis Test with Null Hypothesis H0:μ=14.0 at α=0.10\mathrm { H } _ { 0 } : \mu = 14.0 \text { at } \alpha = 0.10H0​:μ=14.0 at α=0.10

Assume That in a Hypothesis Test with Null Hypothesis $\mathrm { H } _ { 0 } : \mu = 14.0 \text { at } \alpha = 0.10$