364 of 535 randomly selected U.S. adults interviewed said they would not be both

Question

364 of 535 randomly selected U.S. adults interviewed said they would not be bothered if the National Security Agency collected records of personal telephone calls they had made. Is there sufficient evidence to conclude that a majority of U.S. adult feel this way? Test the appropriate hypotheses using a 0.01 significance level. (For z give the answer to two decimal places. For rho give the answer to four decimal places.) The data evidence to suggest that more than half of all U.S. adults say they would not be bothered if the NSA collected records of personal telephone calls they had made.

Explanation / Answer

Hypothesis:

H0 : p < 05

Ha; p >= 0.5

Sample P = 364 / 586 = 0.6212

Test statistic;

z = ( P - p ) / sqrt ( p (1 - p) / n )

= ( 0.6212 - 0.5) / sqrt( 0.5 * 0.5 / 586)

= 5.867

Now, we need to find p value using z = 5.867

p value =  0.00001.

As p value is less than 0.01 so we reject the null hypothesis.

There is sufficient evidence

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