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August 30, 2014

Posted by **carl** on Monday, May 14, 2012 at 9:33am.

115, 128, 107, 109, 116, 124, 135

127, 115, 104, 118, 126, 129, 133

- stat -
**MathGuru**, Monday, May 14, 2012 at 7:01pmNull and alternative hypotheses:

Ho: The population standard deviation is = 15

Ha: The population standard deviation is < 15

Data given:

sample standard deviation = ? (Note: standard deviation is the square root of the variance; therefore, variance is standard deviation squared).

level of significance = 0.10

n = 14

Calculate the standard deviation from the data given.

The test statistic used in making a decision is the chi-square.

Here's the formula:

chi-square = (sample size - 1)(sample variance)/(value specified in the null hypothesis)

Note: Convert both standard deviations to variances when working with the formula.

Degrees of freedom is equal to n - 1, which is 13.

Checking a chi-square table using alpha = 0.10 with 13 degrees of freedom, find the critical value.

If the test statistic exceeds the critical value from the chi-square table, then the null is rejected and you can accept the alternative hypothesis. If the test statistic does not exceed the critical value from the table, then the null cannot be rejected and you cannot conclude a difference.

I hope this will help get you started.

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