Question

ndependent random samples are taken at a university to compare the average GPA of seniors to the average GPA of sophomores. Given a 95% confidence interval for the difference between the true average GPAs (seniors - sophomores) of (0, 1.13), what can you conclude?

Question 9 options:

	1) We are 95% confident that the difference between the two sample GPAs falls within the interval.
	2) We are 95% confident that the average GPA of seniors is greater than the average GPA of sophomores.
	3) There is no significant difference between the true average GPA for seniors and sophomores.
	4) We do not have enough information to make a conclusion.
	5) We are 95% confident that the average GPA of seniors is less than the average GPA of sophomores.

Question 10 (1 point)

The owner of a local golf course wants to estimate the difference between the average ages of males and females that play on the golf course. He randomly samples 24 men and 21 women that play on his course. He finds the average age of the men to be 37.722 with a standard deviation of 7.091. The average age of the women was 32.214 with a standard deviation of 5.243. He uses this information to calculate a 99% confidence interval for the difference in means, (0.436, 10.58). The best interpretation of this interval is which of the following statements?

Question 10 options:

	1) We are certain that the difference between the average age of all men and all women is between 0.436 and 10.58.
	2) We are 99% confident that the difference between the average age of the men and women surveyed is between 0.436 and 10.58
	3) We do not know the population means so we do not have enough information to make an interpretation.
	4) We are 99% sure that the average age difference between all males and females is between 0.436 and 10.58.
	5) We are 99% confident that the difference between the average age of all men and all women who play golf at the course is between 0.436 and 10.58

Answer 1

1)

Given that:

95% confidence interval for the difference between the true average GPAs (seniors - sophomores) is (0, 1.13),

Hence we can conclude that :

We are 95% confident that the difference between the two sample GPAs falls within the interval.

Correct option : (1)

2)Here we have:

99% confidence interval for the difference in means, (0.436, 10.58).

Hence we can conclude that:

We are 99% confident that the difference between the average age of all men and all women who play golf at the course is between 0.436 and 10.58

Correct option (5)