Question

A statistics professor wants to examine the number of hours that seniors and freshmen study for the final. Specifically, the professor wants to test if the average number of hours that seniors study is greater than the average number of hours that freshmen study. If the seniors are considered group 1 and the freshmen are considered group 2, what are the hypotheses for this scenario?

Question 1 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 2 (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 greater than the votes for Candidate 2. What are the hypotheses for this test?

Question 2 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 3 (1 point)

Does the amount of hazardous material absorbed by the bodies of hazardous waste workers depend on gender? You want to test the hypotheses that the amount absorbed by men (group 1) is different from the amount absorbed by women (group 2). A random sample of 212 male workers and 114 female workers showed an average lead absorption in the blood of 12.59 (SD = 1.897) and 12.75 (SD = 0.621), respectively (measured in micrograms/deciliter). Assuming that the population standard deviations are the same, perform a two independent samples t-test on the hypotheses Null Hypothesis: μ₁ = μ₂, Alternative Hypothesis: μ₁ ≠ μ₂. What is the test statistic and p-value of this test?

Question 3 options:

1)	Test Statistic: 0.875, P-Value: 0.3822

2)	Test Statistic: -0.875, P-Value: 1.8089

3)	Test Statistic: -0.875, P-Value: 0.8089

4)	Test Statistic: -0.875, P-Value: 0.3822

5)	Test Statistic: -0.875, P-Value: 0.1911

Question 4 (1 point)

Do sit down restaurant franchises and fast food franchises differ significantly in stock price? Specifically, is the average stock price for sit-down restaurants less than the average stock price for fast food restaurants? A hypothesis test for two independent samples is run on data recorded from the stock exchange and a p-value is calculated to be 0.9051. What is the appropriate conclusion?

Question 4 options:

1)	The average stock price of sit-down restaurants is significantly less than the average stock price of fast food restaurants.

2)	We did not find enough evidence to say a significant difference exists between the average stock price of sit-down restaurants and the average stock price of fast food restaurants.

3)	We did not find enough evidence to say the average stock price of sit-down restaurants is less than the average stock price of fast food restaurants.

4)	The average stock price of sit-down restaurants is greater than or equal to the average stock price of fast food restaurants.

5)	We did not find enough evidence to say the average stock price of sit-down restaurants is greater than the average stock price of fast food restaurants.

Answer 1

Ans:

1)Option 1 is correct.

HO: μ1 ≤ μ2 HA: μ1 > μ2

2)Option 2 is correct.

H_O: μ₁ ≤ μ₂
H_A: μ₁ > μ₂

3)

pooled standard deviationSQRT((211*1.897^2+113*0.621^2)/(212+114-2))=1.574

standard error=1.574*sqrt((1/212)+(1/114))=0.1828

Test statistic:

t=(12.59-12.75)/0.1828=-0.875

df=212+114-2=324

p-value=tdist(0.875,324,2)=0.3822

4)Fail to reject the null hypothesis.

We did not find enough evidence to say the average stock price of sit-down restaurants is less than the average stock price of fast food restaurants.