# Thread: do not understand evidence of a mean

1. ## do not understand evidence of a mean

My problem states:
IQ test scores of 31 seventh-grade girls in a Midwest school district. IQ scores follow a Normal distdribution with standard deviation of 15. Treat these girls as an SRS of all seventh-grade girls in this district. IQ scores in a broad population are supposed to have a mean of 100. Is there evidence that the mean in this district differs from 100? State hypotheses, find the test statistic and its P-value, and state your conclusion.

So far I have the hypotheses as
Ho: mean 100; Ha: mean not equal to 100
Z=2.15

I found the Z* by finding the average/mean.
114 100 104 89 102 91 114 114 103 105
108 130 120 132 111 128 118 119 86 72
111 103 74 112 107 103 98 96 112 112
93/31=105.8

105.8-100/(15/square root of 31))=2.15

Am I on the right track?
I cannot find the P-value!

HELP!

2. Look on your normal chart at the number corresponding to 2.15. you get .9842. 1-.9842=.0158 , which is your p-value. Your decision to reject the null hypothesis will be based on what level of signifigance you want. Here, for a .01 level of sig, you cannot reject the null because .0158>.0100. Or you can look at it like this: 2.33 is the Z corresponding to .01(1-.01=.99) level of sig. Your test stat is smaller than 2.33, therefore does not fall into the rejection region.

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