Question

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 less than the votes for Candidate 2. What are the hypotheses for this test?

	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

Do sit down restaurant franchises and fast food franchises differ significantly in stock price? Specifically, is the average stock price for sit-down restaurants different from the average stock price for fast food restaurants? If sit down restaurants are considered group 1 and fast food restaurants are group 2, what are the hypotheses of this

	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

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 24 men and 24 women that play on his course. He finds the average age of the men to be 31.69 with a standard deviation of 16.373. The average age of the women was 32.09 with a standard deviation of 14.407. 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.

	1) Test Statistic: -0.09, P-Value: 1.0714
	2) Test Statistic: -0.09, P-Value: 0.4643
	3) Test Statistic: 0.09, P-Value: 0.5357
	4) Test Statistic: 0.09, P-Value: 0.4643
	5) Test Statistic: -0.09, P-Value: 0.5357

Do sit down restaurant franchises and fast food franchises differ significantly in stock price? Specifically, is the average stock price for sit-down restaurants different from 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 0.4466. What is the appropriate conclusion?

	1) The average stock price of sit-down restaurants is equal to 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) 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.
	5) The average stock price of sit-down restaurants is significantly different from the average stock price of fast food restaurants.

Answer 1

a) Option - 5) H0:

HA:

b) Option - 5) H0:

HA:

c) The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

= (31.69 - 32.09)/sqrt((16.373)^2/24 + (14.407)^2/24) = -0.09

Df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

= ((16.373)^2/24 + (14.407)^2/24)^2/(((16.373)^2/24)^2/23 + ((14.407)^2/24)^2/23) = 45

P-value = P(T > -0.09)

= 1 - P(T < -0.09)

= 1 - 0.4643 = 0.5357

Option - 5 is correct.

d) Option - 2) We did not 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.