Question

The p-value for a two-sided test of the null hypothesis H0: μ = 10 is 0.06.(a) Would a 95% confidence interval for μ include the value 10? Why?(b) Would a 90% confidence interval for μ include the value 10? Why?

Answer 1

Answer:

a) Yes b) No

Step-by-step explanation:

Given that the p value for a two-sided test of the null hypothesis H0: μ = 10

is 0.06

a) $p value = 0.06.\\Confidence level = 95%\\Significance level = 100-95 = 5%\\Alpha = 0.05\\\\p \geq \alpha is true$

Hence we accept null hypothesis

This implies that 10 will be within the confidence interval of 95%

b) If confidence level = 90%

$\alpha = 0.10\\p value = 0.06\\p \leq 0.10$

So we have to reject null hypothesis.

So we do not have 10 in the confidence interval

The reason is the lower the confidence level, the narrower the confidence interval.  In this case, 10 has gone outside the narrower interval hence we get this.