Question

Question 10 (1 point)

A restaurant wants to test a new in-store marketing scheme in a small number of stores before rolling it out nationwide. The new ad promotes a premium drink that they want to increase the sales of. 14 locations are chosen at random and the number of drinks sold are recorded for 2 months before the new ad campaign and 2 months after. The average difference in nationwide sales quantity before the ad campaign to after (after - before) is 2.9 with a standard deviation of 7. Using this information, they calculate a 95% confidence paired-t interval of (-1.14, 6.94). Which of the following is the best interpretation?

Question 10 options:

	1) We are 95% confident that the average difference in sales quantity between after the ad campaign to before for all restaurants is between -1.14 and 6.94.
	2) The proportion of all stores that had a difference in sales between after the ad campaign to before is 95%.
	3) We are 95% confident that the difference between the average sales after the ad campaign and the average sales before the ad campaign is between -1.14 and 6.94.
	4) We are 95% confident that the average difference in the sales quantity after to before of the stores sampled is between -1.14 and 6.94.
	5) We are certain the average difference in sales quantity between after the ad campaign to before for all stores is between -1.14 and 6.94.

Question 11 (1 point)

Professors in the Economics Department at Western want to determine how challenging the program was for students. Out of a random sample of 24 students, 18 indicated that the program was either "challenging" or "very challenging". The 90% confidence interval estimating the proprotion of all students in the department who thought the program was challenging is given by which of the following?

Question 11 options:

	1) ( 0.60461 , 0.89539 )
	2) ( 0.66161 , 0.83839 )
	3) ( 0.63673 , 0.86327 )
	4) ( -0.60461 , 0.89539 )
	5) ( 0.10461 , 0.39539 )

Question 12 (1 point)

A medical researcher wants to determine if the average number of days spent in the hospital after a certain procedure is greater than 9.3 days. If the researcher conducts a hypothesis test, what will the null and alternative hypotheses be?

Question 12 options:

	1) HO: μ ≤ 9.3 HA: μ > 9.3
	2) HO: μ < 9.3 HA: μ ≥ 9.3
	3) HO: μ = 9.3 HA: μ ≠ 9.3
	4) HO: μ > 9.3 HA: μ ≤ 9.3
	5) HO: μ ≥ 9.3 HA: μ < 9.3

Question 13 (1 point)

A medical researcher wants to determine if the average hospital stay after a certain procedure is less than 14.97 days. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≥ 14.97, Alternative Hypothesis: μ < 14.97. If the researcher randomly samples 26 patients that underwent the procedure and determines their average hospital stay was 15.68 days with a standard deviation of 7.183 days, what is the test statistic and p-value of this test?

Question 13 options:

	1) Test Statistic: 0.504, P-Value: 0.3093
	2) Test Statistic: 0.504, P-Value: 1.3814
	3) Test Statistic: -0.504, P-Value: 0.6907
	4) Test Statistic: -0.504, P-Value: 0.3093
	5) Test Statistic: 0.504, P-Value: 0.6907

Question 14 (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 greater 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 0.4023. What is the appropriate conclusion?

Question 14 options:

	1) The average stock price of sit-down restaurants is less than or equal to the average stock price of fast food restaurants.
	2) The average stock price of sit-down restaurants is significantly greater than 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 greater 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 less than the average stock price of fast food restaurants.
	5) 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.

Answer 1

Answer 10:

3) We are 95% confident that the difference between the average sales after the ad campaign and the average sales before the ad campaign is between -1.14 and 6.94.

Answer 11:

CI (Proportion) = (0.75 - 0.145398832, 0.75 + 0.145398832)

CI (Proportion) = (0.604601, 0.895399)

1) (0.60461 , 0.89539)

Answer 12:

1)

HO: μ ≤ 9.3
HA: μ > 9.3

Answer 13:

Degrees of freedom = n-1 = 26-1 = 25

P-value for t = 0.504 and df = 25 for a left-tailed test is 0.6907 (Obtained using p-value calculator)

5) Test Statistic: 0.504, P-Value: 0.6907

Answer 14:

3) 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.