# Suppose that young adults own an average of three pairs of jeans. Survey eight people from your class. The class size is 30. The sample mean is 30. The standard deviation is 10. Determine if the average is higher than three. Assume the population is normal. Ho=___Ha=___ In words, define the random variable ___ =___ The distribution to use for the test is ____ Determine the test statistic using your data Draw a graph an label it appropriately. Shade the actual level of significance.

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Suppose that young adults own an average of three pairs of jeans. Survey eight people from your class. The class size is 30. The sample mean is 30. The standard deviation is 10. Determine if the average is higher than three. Assume the population is normal.

Ho=___

Ha=___

In words, define the random variable ___ =___

The distribution to use for the test is ____

Determine the test statistic using your data

Draw a graph an label it appropriately. Shade the actual level of significance.

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Step 1

Since the sample size is 8 and the population SD is not known we use the sample SD as an estimate of the population SD. This implies that only t-statistic is used and hence t-distribution is applicable. Also since the population is finite a finite correction factor would be used to calculate the SE of the mean of sampling distribution.

The hypotheses for the problem is as follows:

H0: µ = 3

Ha: µ > 3

Step 2

Determine the appropriate statistical test. The test statistic is given below:

We assume a value of alpha as 0.05 (5% significance level to test the hypothesis).

Degree of freedom, df = n -1 = 8-1 = 7.

This test is one-tailed, and the critical table t value is

t0.05,7 = 1.895

We will reject the null hypothesis if the observed test statistic is greater than 1.895.

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