Question

Suppose a test of H0: μ = 0 vs. Ha: μ ≠ 0 is run with α = 0.05 and the P-value of the test is 0.052. Using the same data, a confidence interval for μ is also constructed.
(a) Of the following, which is the largest confidence level for which the confidence interval will not contain 0?

90%

94%

95%

96%

99%

(b) Of the following, which is the smallest confidence level for which the confidence interval will contain 0?

90%

94%

95%

96%

99%

Answer 1

We have different values asociated here, but easly we can also start

calculating the confidence level from a lower value.

We can define a confidence level of x%, then the asociated level of significance will be

$1-\frac{x}{100}$

Here for $x=(90,94)$

Defining the p-value as 0.052 we have a range between the test reject,

that is,

$1-\frac{x}{100}$, for the p-value

But when we do the calculation we note that if $x=(94,90)$; the test reject $H_0:\mu=0$

That's mean that the asociated confidence interval won't contain 0.

Evaluating for the value of 90 and 94, 90 causes the hypothesis to be rejected immediately, but 94 does not.

The lowest number for this approximation in the response ranges should be the number immediately above 90%, that is, the answer is 94%.