7. (19 Pts) The standard deviation of math test scores at one high school is 16.

Question

7. (19 Pts) The standard deviation of math test scores at one high school is 16.1. The standard deviation of the math scores of a random sample of 22 girls was 14.5. Use a significance level of 0.01 to test whether the standard deviation, o, of all the girl's test scores is smaller than standard deviation of the high school scores. Previous studies have shown that the distribution of the test scores is approximately a normal distribution. NOTE: NO COMPUTATIONS ARE REQUIRED (a) This problem is about (circle the correct one): One population mean Two population means, independent samples Two population means, paired samples One population standard deviation (b) State the null and alternate hypotheses (c) What is the level of significance? (d) List the assumptions and show the numbers or information given to meet each assumption. (e) Circle which of the following Statcrunch methods you would use to test the hypothesis stated in part (b). Z Stats - One sample T Stats - One sample T Stats - Two samples T Stats-Paired Sample Variance tests - One sample None of these since not all assumptions are met (f) If the P-value is 0.2909, show how you determine if Ho is rejected or not. (g) Write the interpretation of the results of the hypothesis test.

Explanation / Answer

Answers:

Part a

One population standard deviation

(We want to check the significance of population standard deviation by using Chi square test.)

Part b

Null hypothesis: H0: = 16.1

Alternative hypothesis: Ha: < 16.1

(Researchers claim suggest that the population standard deviation is less than 16.1)

Part c

Level of significance = = 0.01

(It is already given in the hypothesis test problem.)

Part d

The assumption of normality is given in the problem. It is said that previous studies have shown that the distribution of the test scores is approximately a normal distribution.

Part e

Variance tests – One sample

(Here, we have to use one sample chi square test for variance or standard deviation. Using test for variance or standard deviation is same and gets same results.)

Part f

Here, we are given

P-value = 0.2909

= 0.01

P-value >

So, we do not reject the null hypothesis H0

(We know the decision rule for rejecting the null hypothesis. We reject the null hypothesis if the p-value is less than the given level of significance or alpha value and we do not reject the null hypothesis if the p-value is greater than the given level of significance or alpha value.)

Part g

Here, we do not reject the null hypothesis that the population standard deviation is 16.1.

There is insufficient evidence to conclude that the population standard deviation is less than 16.1.

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