Question

Suppose we test H₀: μ = 42 versus the alternative H_a: μ ≠ 42.   The p-value for this test is 0.03, which is less than 0.05, so the null hypothesis will be rejected.

Suppose that after this test, we form a 95% confidence interval for μ. Which of the following intervals is the only possible confidence interval for these data? (Hint: use chapter 13 and the relationship between confidence intervals and hypothesis tests)

Question 10 options:

	(35, 54)
	(24, 79)
	(37, 41)
	(41, 43)
	(12, 142)

Answer 1

Solution:

Null hypothesis H₀ : μ = 42

Alternative hypothesis H_a :  μ ≠ 42.

Two tailed test

Using p value , the null hypothesis is rejected . (Because p value is less than alpha level)

In confidence interval approach , the null hypothesis is rejected if the hypothetical value is NOT INSIDE THE INTERVAL.

Here hypothetical value is 42

So , from given intervals , only one interval (37 , 41 ) is such that the null hypothesis is rejected.

Correct option is

( 37 , 41 )