Assume that a $95 \%$ confidence interval for the mean is $10.5

Question

Assume that a $95 \%$ confidence interval for the mean is $10.5 < \mu < 15.0$. The null hypothesis $H _ { 0 } : \mu = 12.0$ at $\alpha = 0.05$ would
A) not be rejected because 12.0 is less than 15.0.
B) be rejected because 12.0 is more than 10.5.
C) not be rejected because 12.0 is between 10.5 and 15.0.
D) be rejected because 12.0 is not equal to 12.75.

Quizplus · Accepted Answer

Since 12.0 falls within the confidence interval of 10.5 to 15.0, it suggests that the null hypothesis that $\mu = 12.0$ is plausible and should not be rejected at the $\alpha = 0.05$ level.

Assume That A 95%95 \%95% Confidence Interval for the Mean Is 10.5<μ<15.010.5 < \mu < 15.010.5<μ<15.0

Assume That A $95 \%$ Confidence Interval for the Mean Is $10.5 < \mu < 15.0$