Statistics help needed with hypotheses, z value and z test value

timer Asked: Nov 5th, 2015
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Question Description

Many people believe that the average number of Facebook friends is 130. The population standard deviation is 38.2. A random sample of 50 high school students in a particular county revealed that the average number of Facebook friends was 162. At α = 0.05, is there sufficient evidence to conclude that the mean number of friends is greater than 130?

Tutor Answer

School: Boston College

Thank you for the opportunity to help you with your question!

We have

Null Hypothesis:mean .m <= 130

Alternative hypothesis:Ha,m >130

Find the z test value:-

Given standard deviation,d=38.2

Standard error =d/sqrt (n) =38.2/(50)^(.5)=5.402

Calculating the z test

The critical value for the right end test is 1.645

As the critical z value is less than z test therefore we reject the null hypothesis and accept the alternative hypothesis.

Thus  there is sufficient evidence to conclude that the mean number of friends is greater than 130

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Good stuff. Would use again.

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