If the null hypothesis $H _ { 0 } : \mu = 11.0$ is not rejected at $\alpha = 0.05$ when a mean of $8.0$ is obtained from a random sample, one could also say that
A) the 95% confidence interval for the population mean contains the value 11.0.
B) the 5% confidence interval for the population mean does not contain the value 11.0
C) the 95% confidence interval for the population mean does not contain the value 11.0.
D) the 5% confidence interval for the population mean contains the value 8.0.

Question

Quizplus · Accepted Answer

If the null hypothesis $H_0: \mu = 11.0$ is not rejected, it means that the sample evidence is not strong enough to conclude that the population mean differs from 11.0 at the 5% significance level. This implies that a 95% confidence interval constructed from the sample data would include the value 11.0, as the confidence interval provides a range of values that are considered plausible for the population mean based on the sample data.

If the Null Hypothesis H0:μ=11.0H _ { 0 } : \mu = 11.0H0​:μ=11.0

If the Null Hypothesis $H _ { 0 } : \mu = 11.0$