Question

The owner of a local supermarket wants to estimate the difference between the average number of gallons of milk sold per day on weekdays and weekends. The owner samples 8 weekdays and finds an average of 218.91 gallons of milk sold on those days with a standard deviation of 33.376. 10 (total) Saturdays and Sundays are sampled and the average number of gallons sold is 377.74 with a standard deviation of 49.365. Construct a 99% confidence interval to estimate the difference of (average number of gallons sold on weekdays - average number of gallons sold on weekends). Assume the population standard deviations are the same for both weekdays and weekends.

Question 8 options:

	1) (-179.28, -138.38)
	2) We only have the sample means, we need to know the population means in order to calculate a confidence interval.
	3) (-211.5, -106.16)
	4) (-2733.15, 2415.49)
	5) (-218.55, -99.11)

Question 9 (1 point)

It is believed that using a solid state drive (SSD) in a computer results in faster boot times when compared to a computer with a traditional hard disk (HDD). You sample a group of computers and use the sample statistics to calculate a 99% confidence interval of (1.12, 10.49). This interval estimates the difference of (average boot time (HDD) - average boot time (SSD)). What can we conclude from this interval?

Question 9 options:

	1) We do not have enough information to make a conclusion.
	2) We are 99% confident that the difference between the two sample means falls within the interval.
	3) We are 99% confident that the average boot time of all computers with an SSD is greater than the average of all computers with an HDD.
	4) We are 99% confident that the average boot time of all computers with an HDD is greater than the average of all computers with an SSD.
	5) There is no significant difference between the average boot time for a computer with an SSD drive and one with an HDD drive at 99% confidence.

Question 10 (1 point)

A pharmaceutical company is testing a new drug to increase memorization ability. It takes a sample of individuals and splits them randomly into two groups. After the drug regimen is completed, all members of the study are given a test for memorization ability with higher scores representing a better ability to memorize. Those 21 participants on the drug had an average test score of 24.483 (SD = 4.32), while those 25 participants not on the drug had an average score of 22.121 (SD = 6.091). You use this information to create a 90% confidence interval for the difference in average test score of (-0.302, 5.026). Which of the following is the best interpretation of this interval?

Question 10 options:

	1) We are 90% confident that the difference between the average test score of all people who would take drug and all people not taking the drug is between -0.302 and 5.026.
	2) We are 90% sure that the average difference in test score of all people who would take the drug and people not on the drug in the state the study was completed in is between -0.302 and 5.026.
	3) We are certain that the difference between the average test score of all people who would take drug and all people not taking the drug is between -0.302 and 5.026.
	4) We do not know the population means so we do not have enough information to make an interpretation.
	5) We are 90% confident that the difference between the average test score of people who would take drug in the study and people not on the drug in the study is between -0.302 and 5.026.

Question 11 (1 point)

Disability Services introduced a new mentorship program to help students with disabilities achieve better scholastic results. Test grades were recorded for 27 students before and after the program was introduced. The average difference in test score (after - before) was 9.632 with a standard deviation of 3.293. If Disability Services is interested in creating a 99% confidence interval for the true average difference in test scores, what is the margin of error?

Question 11 options:

	1) 1.761
	2) 0.6337
	3) 1.7559
	4) 1.6325
	5) 1.567

Question 12 (1 point)

Researchers in the corporate office of an airline wonder if there is a significant difference between the cost of a flight on Priceline.com vs. the cost of the same flight on the airline's own website. A random sample of 5 flights were tracked on Priceline.com and the airline's website and the mean difference in price (Priceline.com - Airline Site) was $-65.796 with a standard deviation of $17.3604. Create a 90% confidence interval for the true average difference in costs between the vendors.

Question 12 options:

	1) (82.3472, -49.2448)
	2) (-73.5598, -58.0322)
	3) (-82.3472, -49.2448)
	4) (-67.9278, -63.6642)
	5) (-81.4404, -50.1516)

Question 13 (1 point)

A new drug to treat high cholesterol is being tested by pharmaceutical company. The cholesterol levels for 26 patients were recorded before administering the drug and after. The 90% confidence interval for the true mean difference in total cholesterol levels (after - before) was (-15.31, 15.82). Which of the following is the appropriate conclusion?

Question 13 options:

	1) We are 90% confident that the average difference in cholesterol levels is positive, with the higher cholesterol levels being before the drug regimen.
	2) There is not a significant difference in average cholesterol levels before and after the drug.
	3) We are 90% confident that the average difference in cholesterol levels is negative, with the higher cholesterol levels being before the drug regimen.
	4) We are 90% confident that the average difference in cholesterol levels is positive, with the higher cholesterol levels being after the drug regimen.
	5) We are 90% confident that the average difference in cholesterol levels is negative, with the higher cholesterol levels being after the drug regimen.

Question 14 (1 point)

Automobile manufacturers are interested in the difference in reaction times for drivers reacting to traditional incandescent lights and to LED lights. A sample of 21 drivers are told to press a button as soon as they see a light flash in front of them and the reaction time was measured in milliseconds. Each driver was shown each type of light. The average difference in reaction times (traditional - LED) is 1.6 ms with a standard deviation of 5.61 ms. A 90% confidence interval for the average difference between the two reaction times was (-0.51, 3.71). Which of the following is the best interpretation?

Question 14 options:

	1) The proportion of all drivers that had a difference in reaction times between the two lights is 90%.
	2) We are 90% confident that the difference between the average reaction time for LED lights and the average reaction time for traditional lights is between -0.51 and 3.71.
	3) We are certain the average difference in reaction times between the two light types for all drivers is between -0.51 and 3.71.
	4) We are 90% confident that the average difference in reaction time between the two light types for all drivers is between -0.51 and 3.71.
	5) We are 90% confident that the average difference in the reaction times of the drivers sampled is between -0.51 and 3.71.

Answer 1

Question 8:

For Weekdays

n1 = 8

Sample mean =

Sample standard deviation = s1 = 33.376

For Weekends (Saturday and Sunday)

n2 = 10

Sample mean =

Sample standard deviation = s2 = 49.365

Assume that the population standard deviations are equal.

So we use pooled t interval.

Confidence level = c = 0.99

99% confidence interval to estimate the difference is

Where tc is t critical value for c = 0.99 and degrees of freedom = n1+n2-2 = 8 + 10 - 2 = 16

tc = 2.921                    (From statistical table of z values)

sp is pooled standard deviation

                (Round to 2 decimal)

99% confidence interval to estimate the difference is (-218.56, -99.10)