Question

In: Statistics and Probability

1) An App developing company recently developed a new game that can be played on the...

1)

An App developing company recently developed a new game that can be played on the iPhones. The company wants to run a survey on the satisfaction rate on the game. They randomly send out a survey to 600 iPhone users who have downloaded the app and 498 of them are happy with the game.

What is a 95% Confidence interval for the true proportion that are satisfied with the app companies game?

Group of answer choices

(.76, .89)

(.79, .87)

(.83, .88)

(.80, .86)

2)

Referring back to the scenario in the previous few questions, suppose the app company wanted to make a 99% confidence interval for the true satisfaction rate with a margin of error of 2%.

How big a sample would they need to take?

Group of answer choices

4147.36

3382

3381.42

4148

3)

A video game streamer with a lot of subscribers (say 20,000) wants to switch to a new video game. The streamer will only do this if there is evidence that more that 75% of his subscriber base would be interested in watching the new game. He randomly selects 800 subscribers and asks if they would be interested in watching the new game. 632 say yes. We will do a hypothesis test to assess whether the streamer should switch games.

Identify the correct Null and Alternative Hypotheses.

Group of answer choices

Ho: p = .75 vs Ha: p < .75

Ho: p > .75 vs Ha: p = .75

Ho: p = .79 vs Ha: p > .79

Ho: p = .75 vs Ha: p > .75

4)

A video game streamer with a lot of subscribers (say 20,000) wants to switch to a new video game. The streamer will only do this if there is evidence that more that 75% of his subscriber base would be interested in watching the new game. He randomly selects 800 subscribers and asks if they would be interested in watching the new game. 632 say yes. We will do a hypothesis test to assess whether the streamer should switch games.

The conditions for a hypothesis test are met in this problem. What is the value of the test statistic? (round to two decimals)

Group of answer choices

2.27

1.96

2.78

2.61

5)

A video game streamer with a lot of subscribers (say 20,000) wants to switch to a new video game. The streamer will only do this if there is evidence that more that 75% of his subscriber base would be interested in watching the new game. He randomly selects 800 subscribers and asks if they would be interested in watching the new game. 632 say yes. We will do a hypothesis test to assess whether the streamer should switch games.

Using the test statistic you calculated in the previous question, give the p-value.

Group of answer choices

.0045

.0001

.0056

.0088

Solutions

Expert Solution

1)

They randomly send out a survey to 600 iPhone users who have downloaded the app and 498 of them are happy with the game.

Thus n = 600   and   x = 498

Now estimate of true proportion that are satisfied with the app companies game is

= x /n = 498 / 600 = 0.83

i.e = 0.83

95% Confidence interval C.I for the true proportion that are satisfied with the app companies game is given by

C.I = ( - * , + * )

Here = 0.05 hence   = 1.96

C.I = ( - * , + * )

= (0.83 - 1.96 * , 0.83 + 1.96 * )

C.I = ( 0.7999431 , 0.8600569 ) ( 0.80 , 0.86)

Thus C.I =( 0.80 , 0.86)

Correct Option is option D) ( 0.80 , 0.86)

2)

Company wanted to make a 99% confidence interval for the true satisfaction rate with a margin of error of 2%

Now formula for margin of error M.E is

M.E = *

Given M.E = 0.02 or 2%

          = 0.83   and = 2.58   for = 0.01

Now    ,   M.E = *

= * / M.E

n =( * )2 / M.E2

n = (  2.58 * )2 / ( 0.02)2
   = 0.939218 / 0.022

n = 2348.045

3)

A video game streamer with a lot of subscribers (say 20,000) wants to switch to a new video game.

The streamer will only do this if there is evidence that more that 75% (or 0.75) of his subscriber base would be interested in watching the new game .

Thus null and alternative hypothesis would be

Ho: p = .75       

( no more than mean only 75% of his subscriber base would be interested in watching the new game)

vs

Ha: p > .75  

( more that 75% (or 0.75) of his subscriber base would be interested in watching the new game .

i.e Ho: p = .75 vs Ha: p > .75

Here Rejection of null hypothesis means there are evidence that more than 75% subscriber would be interested in watching the new game .

4)

A video game streamer with a lot of subscribers (say 20,000) wants to switch to a new video game. The streamer will only do this if there is evidence that more that 75% of his subscriber base would be interested in watching the new game.

He randomly selects 800 subscribers and asks if they would be interested in watching the new game. 632 say yes. We will do a hypothesis test to assess whether the streamer should switch games.

Here n = 800   and   x = 623

Thus, = x /n = 632 / 800 = 0.79

= 0.79

To test

Ho: p = .75      vs    Ha: p > .75  

Test Statistics :

T.S =

       =

       = 0.04 / 0.01440052

       = 2.777677

Thus , value of the test statistic is 2.78

5)

Using the test statistic you calculated in the previous question, give the p-value

Thus

P-value   = 2*P( X > T.S )                , where X ~ N(0,1)

                 = 2*P( X > 2.78)    

               = 2*0.0028

                 = 0.0056


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