1. A random sample is obtained from a normal population with variance 2 = 625, a

Question

1. A random sample is obtained from a normal population with variance 2 = 625, and the sample mean is computed. Test the null hypothesis H0: = 100 versus the alternative hypothesis H1: > 100 with = 0.05. Compute the critical value Xc and state your decision rule for each of the following options. H_0: =100 variance ^2=625 =0.05

Sample size n=25

I know that zalpha=1.645 is found using a standard normal table.

xc=100+(1.645)(%)=108.2243 so my decision rule would be to reject if x is greater than 108.2243

BUT I am clueless as how you find that zalpha is 1.645 please explain in detail and clearly.

Explanation / Answer

Hi! You can use a table or technology to get z = 1.645.

Note atht alpha = 0.05, right tailed, so the z score has a left tailed area of 1 - 0.05 = 0.95.

Say, in Excel, you can type on any cell,

=NORMSINV(0.95)

to get z = 1.644853627.

You can also find other standard normal distribution calculators in the internet.

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You can also use the STANDARD NORMAL DISTRIBUTION TABLE.

There, you will see that a left tailed area of 0.95 is exactly betwen 1.64 and 1.65, so it is 1.645 in intreplation.

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