Question

The owner of a local golf course wants to examine the difference between the average ages of males and females that play on the golf course. Specifically, he wants to test if the average age of males is less than the average age of females. If the owner conducts a hypothesis test for two independent samples and calculates a p-value of 0.1447, what is the appropriate conclusion? Label males as group 1 and females as group 2.

The average age of males is greater than or equal to the average age of females.

We did not find enough evidence to say the average age of males is less than the average age of females.

The average age of males is significantly less than the average age of females.

We did not find enough evidence to say the average age of males is larger than the average age of females. We did not find enough evidence to say a significant difference exists between the average age of males and females.

A medical researcher wants to determine if the average hospital stay of patients that undergo a certain procedure is less than 6.9 days. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≥ 6.9, Alternative Hypothesis: μ < 6.9. If the actual mean is 9.5 days and the null hypothesis is rejected, did a type I, type II, or no error occur?

We do not know the p-value, so we cannot determine if an error has occurred.

Type I Error has occurred.

We do not know the degrees of freedom, so we cannot determine if an error has occurred.

No error has occurred.

Type II Error has occurred

Answer 1

Answer

(A) p value is 0.1447, which is greater than significance level of 0.05 or 0.10. So, result is insignificant and we can never fail reject null hypothesis in this case.

option B is correct answer because there is insufficient evidence to support the test statment

We did not find enough evidence to say the average age of males is less than the average age of females.

(B) Null hypothesis is stating that the mean is greater than or equal to 6.9 and 9.5 is greater than 6.9. So, null hypothesis should not be rejected in this case, but we have rejected the null hypothesis.

so, this is a case of rejecting the true null hypothesis. This means this is a case of type I error because type I error means rejection of a true null hypothesis

Correct answer is

Type I Error has occurred.