Question

We're analyzing the proportion of people watching TV in a given night. In our sample, we have 35 out of 100 people watching TV. We're testing the null hypothesis that 50% of the entire population which we sampled watched TV that night, and got a p-value of 0.00352. What is the conclusion that we make if our significance level was 0.05?

reject the null hypothesis

Based on the above, what would be the p-value associated with the null hypothesis that more than 50% of the people watch TV on this night?

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Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p 0.50

n = 100

x =35

= x / n = 35 / 100 =0.35

P0 = 0.50

1 - P0 = 1 - 0.50 = 0.50

Test statistic = z

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

=0.35 - 0.50 / [(0.50*0.50) / 100 ]

= - 3.00

Test statistic = z = - 3.00

P(z > - 3.00 ) = 1 - P(z < ) = 1 - 0.0013

P-value = 0.9987

= 0.05

P-value >

0.9987 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that