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# ****PLEASE ANSWER ALL QUESTIONS**** Question 12 (1 point) A medical researcher wants to determine if the...

Question 12 (1 point)

A medical researcher wants to determine if the average hospital stay of patients that undergo a certain procedure is greater than 8.7 days. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 8.7, Alternative Hypothesis: μ > 8.7. If the researcher takes a random sample of patients and calculates a p-value of 0.0942 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

Question 12 options:

 1) We did not find enough evidence to say the true average hospital stay of patients is shorter than 8.7 days.
 2) The true average hospital stay of patients is significantly longer than 8.7 days.
 3) We did not find enough evidence to say the true average hospital stay of patients is longer than 8.7 days.
 4) The true average hospital stay of patients is shorter than or equal to 8.7 days.
 5) We did not find enough evidence to say a significant difference exists between the true average hospital stay of patients and 8.7 days.

Question 13 (1 point)

Suppose you work for a political pollster during an election year. You are tasked with determining the projected winner of the November election. That is, you wish to determine if the number of votes for Candidate 1 is different from the votes for Candidate 2. What are the hypotheses for this test?

Question 13 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 14 (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 14 options:

 1) Test Statistic: 0.798, P-Value: 0.4284
 2) Test Statistic: -0.798, P-Value: 0.2142
 3) Test Statistic: 0.798, P-Value: 0.2142
 4) Test Statistic: 0.798, P-Value: 0.7858
 5) Test Statistic: -0.798, P-Value: 0.7858

Question 15 (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 different from 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 0.7073. What is the appropriate conclusion?

Question 15 options:

 1) The average score of students who study one week before a test is equal to 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) We did not find enough evidence to say the average score of students who study one week before a test is greater 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 significantly different from the average score of students who wait to study until the night before a test.
 5) We did not find enough evidence to say a significant difference exists between the average score of students who study one week before a test and the average score of students who wait to study until the night before a test.

Question 16 (1 point)

A new gasoline additive is supposed to make gas burn more cleanly and increase gas mileage in the process. Consumer Protection Anonymous conducted a mileage test to confirm this. They took a sample of their cars, filled it with regular gas, and drove it on I-94 until it was empty. They repeated the process using the same cars, but using the gas additive. Using the data they found, they performed a paired t-test with data calculated as (with additive - without additive) with the following hypotheses: Null Hypothesis: μD ≥ 0, Alternative Hypothesis: μD < 0. If they calculate a p-value of 0.0109 in the paired samples t-test, what is the appropriate conclusion?

Question 16 options:

 1) The average difference in gas mileage is significantly less than 0. The average gas mileage was higher without the additive.
 2) We did not find enough evidence to say there was a significantly negative average difference in gas mileage. The additive does not appear be effective.
 3) The average difference in gas mileage is greater than or equal to 0.
 4) The average difference in gas mileage is significantly different from 0. There is a significant difference in gas mileage with and without the additive.
 5) The average difference in gas mileage is significantly larger than 0. The average gas mileage was higher with the additive.

Question 17 (1 point)

In the year 2000, the average car had a fuel economy of 20.9 MPG. You are curious as to whether the average in the present day is less than the historical value. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≥ 20.9, Alternative Hypothesis: μ < 20.9. If the true average fuel economy today is 22.1 MPG and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Question 17 options:

 1) We do not know the p-value, so we cannot determine if an error has occurred.
 2) Type I Error has occurred.
 3) No error has occurred.
 4) We do not know the degrees of freedom, so we cannot determine if an error has occurred.
 5) Type II Error has occurred

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