Question

Researchers report a 95% CI = 1.41 to 7.62. What would the decision be for a hypothesis test if the null hypothesis were the following?

(a)    μ = 0

Retain the null hypothesis

OR

Reject the null hypothesis.    

(b)    μ = 5

Retain the null hypothesis.

OR

Reject the null hypothesis.    

(c)    μ = 8

Retain the null hypothesis.

OR

Reject the null hypothesis.    

Answer 1

Answer

We know that we reject null hypothesis, when the confidence interval includes the null hypothesis value and we failed to reject the null hypothesis, when the confidence interval didn't include null hypothesis value.

(a) Confidence interval is 1.41 to 7.62 and null hypothesis value is 0, i.e. null hypothesis value is outside the confidence interval range. So, we will reject the null hypothesis because result is statistically significant.

(b) Confidence interval is 1.41 to 7.62 and null hypothesis value is 5, i.e. null hypothesis value is inside the confidence interval range. So, we failed to reject the null hypothesis or retain the null hypothesis because result is insignificant.

(C) Confidence interval is 1.41 to 7.62 and null hypothesis value is 8, i.e. null hypothesis value is outside the confidence interval range. So, we will reject the null hypothesis because result is statistically significant.