Question

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.

.0045

.0001

.0088

.0056

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p =0.75

Ha : p > 0.75

= x / n = 632/800=0.79

1 - P0 = 1-0.75=0.25

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.79-0.75 / [(0.75*0.25) /800 ]

= 2.61

Test statistic = z =2.61

P(z > 2.61) = 1 - P(z < 2.61) = 1-0.9955=0.0045

P-value = 0.0045