Question

Part A:

Suppose you work for a pharmaceutical company that is testing a new drug to treat ulcerative colitis. You conduct a random sample of 34 patients on the new drug and 14 of them indicated a decrease in symptoms since starting the drug regimen. You construct a 90% confidence interval for this proportion to be ( 0.2733 , 0.5502 ). What is the correct interpretation of this confidence interval?

	1) We are certain that 90% of patients will be between 0.2733 and 0.5502.
	2) We are 90% confident that the proportion of patients surveyed that have experienced a reduction in symptoms is between 0.2733 and 0.5502.
	3) We are 90% confident that the proportion of all patients on the drug regimen that have experienced a reduction in symptoms is between 0.2733 and 0.5502.
	4) We cannot determine the proper interpretation of this interval.
	5) We are 90% confident that the proportion of patients who should be on this drug is between 0.2733 and 0.5502.

Part B:

A company seeks to employ a new public relations manager. The hiring committee surveys 15 public relations managers and finds the average salary is $95157.334 with standard deviation of $1895.2408. What is the 95% confidence interval for the true average public relations manager salary?

	1) ( 94114.531 , 96200.137 )
	2) ( 95155.189 , 95159.479 )
	3) ( 94667.985 , 95646.683 )
	4) ( -94107.785 , 96206.883 )
	5) ( 94107.785 , 96206.883 )

Part C:

You read an article in Golf Digest that someone with your average drive distance will have an average score of 84.71. You keep track of your scores for the next 10 rounds and see that your average score is 76.81 with a standard deviation of 2.939 strokes. You create a 90% confidence interval for your average score and it is (75.11, 78.51). Given this information, what is the best conclusion?

	1) The average score does not significantly differ from 84.71.
	2) We are 90% confident that your average score is less than 84.71.
	3) We are 90% confident that your average score is greater than 84.71.
	4) We cannot determine the proper interpretation based on the information given.
	5) The percentage of rounds in which you score more than 84.71 is 90%.

Part D

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. One group is administered the drug, and the other is given a placebo. 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. You are presented a 95% confidence interval for the difference in population mean scores (with drug - without drug) of (0.5, 11.26). What can you conclude from this interval?

	1) We are 95% confident that the difference between the two sample means falls within the interval.
	2) We are 95% confident that the average memorization ability of those on the drug is higher than those who are not on the drug.
	3) We do not have enough information to make a conclusion.
	4) There is no significant difference between the average memorization abilities for those on the drug compared to those not on the drug.
	5) We are 95% confident that the average memorization ability of those not on the drug is higher than those who are on the drug.

Answer 1

A)

option 3 is correct:

We are 90% confident that the proportion of all patients on the drug regimen that have experienced a reduction in symptoms is between 0.2733 and 0.5502.

B)

x= sample mean sample size sample std deviation 95157.3340 15.00 1895.241 SE standard errror of mean = Sx=s/Vn= 489.3491 for 95% Cl; and 14 degree of freedom, value of t= margin of error E=t*std error lower confidence bound=sample mean-margin of error = Upper confidence bound=sample mean+margin of error= 2.1450 1049.654 94107.68 96206.99

option 5 is correct

C)

option 2 is correct

We are 90% confident that your average score is less than 84.71.

D)option 2 is correct (as CI contains only positive values

We are 95% confident that the average memorization ability of those on the drug is higher than those who are not on the drug.