Test the given claim. Use the P-value method or the traditional method. Assume t

Question

Test the given claim. Use the P-value method or the traditional method. Assume that the population is normally distributed and that the sample has been randomly selected 7) For randomly selected adults, IQ scores are normally distributed with a standard deviation of 15. The scores of 4 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of 1Q scores of college students is less than 15. Round the sample standard deviation to three decimal places. 115 128 107 109 116 124 135 127 115 104 118 126 129 133

Explanation / Answer

Solution:

Here, we have to use Chi square test for population standard deviation or variance. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The standard deviation of IQ scores of college students is 15.

Alternative hypothesis: Ha: The standard deviation of IQ scores of college students is less than 15.

H0: = 15 versus Ha: < 15

This is a one tailed test. (Lower tailed or left tailed)

From given sample, we have

Sample size = n = 14

Sample standard deviation = S = 9.819

Degrees of freedom = n – 1 = 14 – 1 = 13

Level of significance = = 0.10

Test statistic is given as below:

Chi square = (n – 1)*S^2/^2

Chi square = (14 - 1)*9.819^2/15^2

Chi square = 5.570515

P-value = 0.0396 (by using Chi square table or excel)

= 0.10

P-value < = 0.10

So, we reject the null hypothesis that the standard deviation of IQ scores of college students is 15.

There is sufficient evidence to conclude that the standard deviation of IQ scores of college students is less than 15.

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