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A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. For this to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network will keep its current lineup of shows unless the majority of the customers want to watch the new show. The network receives 827 responses, of which 428 indicate that they would like to see the new show in the lineup.

b. Calculate the value of the test statistic and the pp-value.

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Considering this task we know that hypotheses look like this:

H0:p0.50HA:p>0.50\begin{aligned} H_0&:p\leq0.50\\ H_A&:p>0.50 \end{aligned}

and we have the sample of n=827n = 827 surveyed users of which x=428x=428 of them indicate that they would like to see the new show in the lineup.

We need to calculate the pp- value and value of the test statistic.

How can we find a statistic value test for the population proportion? Under what conditions is this test statistic feasible?

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