Question

***PLEASE ONLY ANSWER G-K*****

A company which produces video enhancements to concerts seeks to prove, with at least 95% certainty, that video enhancement is worth it. Three interns each independently do a study which proves this.

The first intern decides to survey people who have seen concerts if they would pay to see the band play again within 6 months, and wants the percentage of those who see concerts with video enhancements again to beat the percentage of those who would see video-free concerts by more than 4%. He surveys a total of 290 people who were at non-video-enhanced concerts, of whom 94 say they would do so. He also surveys a total of 260 people who were at video-enhanced concerts of whom 113 say they would do so.

a) Write H0, HA, and the alpha level.

b) Write and label the values of pno video and pvideo Round to the 0.000001.

c) What is the Standard Deviation of the Sample Mean Difference.?

d) Run a Z-test. What is the P-value? Round to the 0.001.

e) Based on this, can the company claim that wants the percentage of those who see concerts with video enhancements beats the percentage of those who would see video-free concerts by more than 4%?

f) [8] Generate a 95% confidence interval regarding the regarding how much higher the % of people who would pay to again see within 6 months video-enhanced concerts is than the % of people would do so for non-video-enhanced concerts. Round to the 0.1%.

The second intern follows a band that sometimes does video-enhanced concerts and sometimes does non-enhanced ones, and asks people to rate the concerts they just saw on a 1-to-10 scale, where 10 is the best.

She wants to prove that, on average people rate concerts more than 1 higher when there is video enhancement.

People who saw non-video-enhanced concerts.

5, 8, 3, 5, 3, 4, 6, 5, 7, 10, 1, 2, 6, 4, 5, 8, 2, 3, 9, 4, 5, 4, 2, 8, 10, 2, 4,

People who saw video-enhanced concerts.

4, 5, 9, 8, 10, 8, 6, 9, 4, 7, 10, 9, 5, 8, 9, 2, 10, 8, 10, 5, 3, 7, 6, 8, 9, 4, 8, 3, 8, 5, 8, 6, 10

g) Write H0, HA, and the alpha level.

h) Run the appropriate type of 2-sample T-test on Graphpad. What is the p-value? Round to the 0.001.

i) Based on this survey, can the company claim that, on average people rate video-enhanced concerts higher by more than one? (For credit, your answer must be both correct and consistent with your answer

to part g above.)

j) Generate a 90% confidence interval regarding the regarding how much higher people, on average, rate video-enhanced concerts. Round to the 0.1.

k) You are the third intern! You estimate that you only have the resources to survey 20 people. Should you do a paired test or an unpaired test? Whichever one you choose, state whether it is paired or unpaired and then describe what you are doing in adequate detail. Your description should make it clear to the reader whether the test is paired or unpaired, and should be plausible and reasonable.

Answer 1

(h) We run a Independent sample t-test on the given data with the assumption of equal population variances of the video enhanced and non-video enhanced populations.

The p-value is 0.059

(i) SInce p-value < 0.10 which the level of significance, we reject the null hypothesis and conclude that on an average, people rate video enhanced concerts more than 1 higher than the non-video enhanced concerts.

(j) A 90% Confidence interval regarding how much higher people, on average, rate video-enhanced concerts, that is for the difference in the mean ratings for the two populations is (0.9436153, infinity)

(k) Now, if we are to take the ratings from a group of 20 individuals only, we will carry out a paired sample t-test, since the ratings for each individual will be correlated for the simple reason that they are from the same person.