Statistics: A claim is made that average grade is 78.3.

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NYC300Z

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The claim is made that the average grade in a statistics class is 78.3. A sample of 38 students gave a sample mean of 74.3. The population has a standard deviation of sigma = 14.

a) Test this claim at alpha equals 0.02
b) Construct a 98% confidence interval for mu (the mean right?)
c) Are the results in a and b the same? Why or why not?
d) For what values of xbar will h0 (hypothesis0:?) be rejected?

okay so I got that
n=38
sigma =14
alpha 0.02

I'm really stuck on how to start any help would be appreciated. Thanks
 
Read your problem. It claims the mean IS. Which implies a two-tail test.

\(\displaystyle \L\\H_{0}:{\mu}=78.3\)

\(\displaystyle \L\\H_{a}:{\mu}\neq{78.3}\)

Because n>30, you can use the population standard deviation, which is 14.

By the way, are you sure about that 14?. As TKH pointed out, that's unusually high.

If it would've said, "Less than" or "more than", then it would've been a one-tail.

At \(\displaystyle {\alpha}=0.02\), your z-score is -2.054 and 2.054.

The rejection region is z<-2.054 and z>2.054.

\(\displaystyle \L\\z=\frac{\overline{x}-{\mu}}{\frac{{\sigma}}{sqrt{n}}}\)

Run your calculations. If z is in the rejection region, reject the null hypothesis. If it's not in the rejection region, do not reject the null hypothesis.
 
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