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

Statistics
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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?

Nov 5th, 2015

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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Nov 5th, 2015

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