The standard deviation score on a certain achievement test at the turn of the ce

Question

The standard deviation score on a certain achievement test at the turn of the century was 20. However, national standards have been implemented which may lead to a change in the standard deviation score. A random sample of 24 scores on this test taken this year yielded the following data set. At a 10% significance level, test the claim that the standard deviation of all current test scores is less than the standard deviation in 2000.

85 77 74 88 89 66 58 76 86 89 73 82 82 82 80 76 87 76 72 49 73 75 82 18

a. Give the null and alternative hypotheses for this test in symbolic form. H0: H1:

b. Determine the value of the test statistic.

c. Determine the appropriate critical value(s).

d Detemine the P-value.

e. Based upon your work above, should you "Reject the null hypothesis" or "Fail to reject the null hypothesis?"

f. Is there sufficient statistical evidence to support the claim that the standard deviation score is now less than 30? Explain your reasoning.

Explanation / Answer

(a) H0 : = 0 = 20

Ha : < 0 = 20

(b) Here the sample standard deviation s = 15.4159

n = 24

the test statistic

We will use chi- square test here

X2 = (n-1) (s/ 0 )2 = (24-1) (15.4159/20)2 = 13.665

so here criitical value of X2 for dF = 23 and alpha = 0.10

as the test is one tailed test so,

X2critical = X20.90,23 = 14.848

so here X2 < X2critical

so we shall reject the null hypothesis and can conclude that that the standard deviation of all current test scores is less than the standard deviation in 2000.

(f) Yes, as there sufficient statistical evidence to support the claim that the standard deviation score is now less than 30 as the standard deviation is less than 20 so it would be less than 30 also.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.