Question

A medical researcher wants to determine if the average hospital stay of patients that undergo a certain procedure is greater than 9.1 days. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 9.1, Alternative Hypothesis: μ > 9.1. If the researcher takes a random sample of patients and calculates a p-value of 0.2003 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

Question 5 options:

1)	The true average hospital stay of patients is significantly longer than 9.1 days.

2)	We did not find enough evidence to say a significant difference exists between the true average hospital stay of patients and 9.1 days.

3)	We did not find enough evidence to say the true average hospital stay of patients is longer than 9.1 days.

4)	We did not find enough evidence to say the true average hospital stay of patients is shorter than 9.1 days.

5)	The true average hospital stay of patients is shorter than or equal to 9.1 days.

Question 6 (1 point)

You are interested in whether the average lifetime of Duracell AAA batteries is different from the average lifetime of Energizer AAA batteries. If Duracell is considered group 1 and Energizer group 2, what are the hypotheses for this test?

Question 6 options:

1)	HO: μ1 ≠ μ2 HA: μ1 = μ2

2)	HO: μ1 ≥ μ2 HA: μ1 < μ2

3)	HO: μ1 ≤ μ2 HA: μ1 > μ2

4)	HO: μ1 > μ2 HA: μ1 ≤ μ2

5)	HO: μ1 = μ2 HA: μ1 ≠ μ2

Question 7 (1 point)

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 is if the average age of males is greater than the average age of females. Assuming males are considered group 1 and females are group 2, this means the hypotheses he wants to tests are as follows: Null Hypothesis: μ₁ ≤ μ₂, Alternative Hypothesis: μ₁ > μ₂. He randomly samples 30 men and 26 women that play on his course. He finds the average age of the men to be 34.26 with a standard deviation of 16.767. The average age of the women was 30.53 with a standard deviation of 18.195. If the owner conducts a hypothesis test, what is the test statistic and what is the p-value? Assume the population standard deviations are the same.

Question 7 options:

1)	Test Statistic: 0.798, P-Value: 0.2142

2)	Test Statistic: -0.798, P-Value: 0.7858

3)	Test Statistic: -0.798, P-Value: 0.2142

4)	Test Statistic: 0.798, P-Value: 0.4284

5)	Test Statistic: 0.798, P-Value: 0.7858

Question 8 (1 point)

You are interested in whether the average lifetime of Duracell AAA batteries is greater than the average lifetime of Energizer AAA batteries. You lay out your hypotheses as follows: Null Hypothesis: μ₁ ≤ μ₂, Alternative Hypothesis: μ₁ > μ₂. After running a two independent samples t-test, you see a p-value of 0.6598. What is the appropriate conclusion?

Question 8 options:

1)	We did not find enough evidence to say a significant difference exists between the average lifetime of Duracell AAA batteries and the average lifetime of Energizer AAA batteries.

2)	We did not find enough evidence to say the average lifetime of Duracell AAA batteries is greater than the average lifetime of Energizer AAA batteries.

3)	The average lifetime of Duracell AAA batteries is significantly greater than the average lifetime of Energizer AAA batteries.

4)	The average lifetime of Duracell AAA batteries is less than or equal to the average lifetime of Energizer AAA batteries.

5)	We did not find enough evidence to say the average lifetime of Duracell AAA batteries is less than the average lifetime of Energizer AAA batteries.

Question 9 (1 point)

It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before. Suppose you want to test the hypothesis that students who study one week before score less than students who study the night before. A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.0362. What is the appropriate conclusion?

Question 9 options:

1)	The average score of students who study one week before a test is significantly different from the average score of students who wait to study until the night before a test.

2)	We did not find enough evidence to say the average score of students who study one week before a test is less than the average score of students who wait to study until the night before a test.

3)	The average score of students who study one week before a test is significantly less than the average score of students who wait to study until the night before a test.

4)	The average score of students who study one week before a test is greater than or equal to the average score of students who wait to study until the night before a test.

5)	The average score of students who study one week before a test is significantly greater than the average score of students who wait to study until the night before a test.

Answer 1

Answer :

Q.5 Since, p-value >0.05

We fail to reject the null hypothesis.

We did not find enough evidence to say a significant difference exists between the true average hospital stay of patients and 9.1 days.

Q.6

HO: μ1 = μ2
HA: μ1 ≠ μ2

Q.8.   We did not find enough evidence to say the average lifetime of Duracell AAA batteries is greater than the average lifetime of Energizer AAA batteries.

Q.9. The average score of students who study one week before a test is significantly different from the average score of students who wait to study until the night before a test.

Q.7