Scores on a national exam assume a normal distribution with a population mean of

Question

Scores on a national exam assume a normal distribution with a population mean of 52 and population standard deviation of 10 points. A sample of 36 exam scores was selected from UCA with a mean score of 48 points. Using a significance level of 0.05, determine whether scores on the exam have actually decreased, statistically. Have the exam scores decreased, statistically? a. No, scores have not decreased. b. Yes, scores have decreased, accept the null hypothesis c. Yes, scores have decreased, reject the null hypothesis d. No, scores have not decreased, accept the null hypothesis

Explanation / Answer

8) null hypothesis = U = 52

alternate hypothesis = u<52

as the distribution = normal therefore the z table can be used

now we have alpha = 0.05

therefore for left tailed test

the critican region = z<=1.96

test static = (48-52)/(10/sqrt(36))

= -2.40

as the z = -2.40<-1.96

therefore we will reject the null hypothesis

conclude scores have decreased

therefore option C is correct

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