146 (a) Using a significance level of 5%, test the hypothesis that the four maga

Question

146

(a) Using a significance level of 5%, test the hypothesis that the four magazine types have the same average length.

(b)Eliminate one magazine type that you now feel has an average length different than the others. Redo the hypothesis test, testing that the remaining three averages are statistically the same. Use a new solution sheet. Based on this test, are the average lengths for the remaining three magazines statistically the same?

(c)Which two magazine types do you think have the same variance in length?

(d)Which two magazine types do you think have different variances in length?

Home Decorating News Health Computer 172 87 82 104 286 94 153 136 163 123 87 98 205 106 103 207 197 101 96

146

Explanation / Answer

Solution :

The average length of all the four magazines =( 204.60 + 102.20 + 104.20 + 138.20 ) / 4

The average length of all the four magazines =549.20/4

The average length of all the four magazines = 137.30

a) H0 : The average lenght of home decorating magazine = 137.20

H1 : The average length of home decorating magazine is not equal to 137.20

Z = X - mean / SD

Variance = 67.40 2 + -352 + -332 + 12

Variance = 1714.44

Sd = 41.40

Z = 204.60 - 137.20 / 41.40

Z = 1.62

At 5% significance level , the value of Z is 1.96 and the calculated value of Z = 1.62 which is less than +/- (1.96) . Hence the null hypothesis for home decorating magazine can be expected .

H0 : The average length of News magazine = 137.20

H1 : The average length of News magazine is not equal to 137.20

Z = 102.20 - 137.20 / 41.40

Z = -0.845

At 5% significance level , the value of Z is 1.96 and the calculated value of Z = -0.845 which is less than +/- (1.96) . Hence the null hypothesis for News magazine can be expected.

H0 : The average length of Health magazine = 137.20

H1 : The average length of Health magazine is not equal to 137.20

Z = 104.20 - 137.20 / 41.40

Z = -0.7971

At 5% significance level , the value of Z is 1.96 and the calculated value of Z = -0.7971 which is less than +/- (1.96) . Hence the null hypothesis for health magazine can be expected.

H0 : The average length of computer magazine = 137.20

H1 : The average length of computer magazine is not equal to 137.20

Z = 138.20 - 137.20 / 41.40

Z = 0.0241

At 5% significance level , the value of Z is 1.96 and the calculated value of Z = 0.0241which is less than +/- (1.96) . Hence the null hypothesis for computer magazine can be expected.

--------------------------------------------------------------------------------------------------------------------------------

Eliminating home decorating magazine

Average length = 344.60 / 3

Average length = 114.86

Variance = -12.662 + -10.662 + 23.342 / 3

variance = 272.88

SD = 16.51

H0 : The average length of News magazine = 114.86

H1 : The average length of News magazine is not equal to 114.86

Z = 102.20 - 114.86 / 16.51

Z = -0.766

At 5% significance level , the value of Z is 1.96 and the calculated value of Z = -0.766 which is less than +/- (1.96) . Hence the null hypothesis for News magazine can be expected.

H0 : The average length of Health magazine = 114.86

H1 : The average length of Health magazine is not equal to 114.86

Z = 104.20 - 114.86 / 16.51

Z = -0.6456

At 5% significance level , the value of Z is 1.96 and the calculated value of Z = -0.6456 which is less than +/- (1.96) . Hence the null hypothesis for health magazine can be expected.

H0 : The average length of computer magazine = 114.86

H1 : The average length of computer magazine is not equal to 114.86

Z = 138.20 - 114.86 / 16.81

Z = 1.388

At 5% significance level , the value of Z is 1.96 and the calculated value of Z =  1.388 which is less than +/- (1.96) . Hence the null hypothesis for computer magazine can be expected.

c) News and health magazine have approximately the same variance in length.

d) Home decorating and computer magazine have different variances in length

Home decorating News Health Computer 172 87 82 104 286 94 153 136 163 123 87 98 205 106 103 207 197 101 96 146 Total 1023 511 521 691 Average Length 204.6 102.2 104.2 138.2

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