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# Testing a Null Hypothesis on a Random Sample of 100

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In the following exercises we consider using a random sample of 100 measurements to test null hypothesis: u=80 versus alternative hypothesis: u>80

8.16 If mean x =85 and standard deviation =20, calculate the value of the test statistic z.

8.18 Use a rejection point to test null hypothesis versus alternate hypothesis by setting probability of Type I error equal to .05

8.20 Use a rejection point to test null hypothesis versus alternate hypothesis by setting probability of Type I error equal to .001

8.52 Suppose that a random sample of nine measurements from a normally distributed population gives a sample mean of x = 2.57 and a sample standard deviation of s = .3. Use rejection points to test null hypothesis : u= 3 versus alternate hypothesis: u does not equal 3 using levels of significance a= .10, a=.05, a=.01, and a=.001. What do you conclude at each value of a?

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#### Solution Preview

Please see the attached file.

In the following exercises we consider using a random sample of 100 measurements to test

null hypothesis: u=80 versus alternative hypothesis: u>80

8.16 If mean x =85 and standard deviation =20, calculate the value of the test statistic z.
Solution:
The Z-statistics for testing a single population mean is given by the formula,

Z =

|Z| = 2.5

8.18 Use a rejection point to test null hypothesis versus alternate hypothesis by setting probability of Type I error equal to .05

Solution:
When the type I error (since the test is two sided we have ) the critical value from the Z-table is 1.96. Since the decision rule is "reject the null hypothesis when Z-test statistics value is greater than Z-table value", we reject the null ...

#### Solution Summary

Solution attaches a .doc file showing how to perform these testing requirements.

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