A company wanted to compare the distance traveled by golf balls produced using e

Question

A company wanted to compare the distance traveled by golf balls produced using each of four different designs. Five balls with each design were brought to a golf course for testing. The order in which the balls were hit with the same club from the first tee was randomized so that the tester did not know which type of ball was being hit. In the time it took to hit all 20 balls, the environmental conditions were essentially the same. The results (distance traveled in yards) for the four designs are provided below.

Complete parts a and b.

Design 1               Design 2               Design 3               Design 4

213.76                   221.91                   219.20                   226.42

203.40                   223.66                   228.09                   226.03

209.19                   208.93                   224.05                   222.64

201.27                   222.16                   230.32                   237.30

208.36                   216.87                   224.93                   226.91

a. At the 0.01 level of significance, is there evidence of a difference in the median distances traveled by the golf balls with different designs?

Define Mj as the median of the jth independent group (for this problem, Design j).

State the null and alternative hypotheses.

H0: (M1=M2=M3=M4=M5, Not all Mj are equal (where j=1, 2, 3, 4, 5), M1=M2=M3=M4, M1M2M3M4M5, M1M2M3, Not all Mj are equal (where j=1, 2, 3,4)

H1: (M1=M2=M3=M4=M5, Not all Mj are equal (where j=1, 2, 3, 4, 5), M1=M2=M3=M4, M1M2M3M4M5, M1M2M3, Not all Mj are equal (where j=1, 2, 3, 4)

Determine the test statistic.

The test statistic is ___? (Round to three decimal places as needed.)

Calculate the p-value.

The p-value is ____? (Round to three decimal places as needed.)

Choose the correct answer below.

Since the test statistic is (greater than or equal to, less than) than the level of signifiance, (do not reject, reject) H0. There is (insufficient, sufficient) evidence of a significant difference in the median distances traveled among the different designs.

b. A one-way ANOVA of the same data gives F =15.546 with p-value = 0.000.

Compare the results in (a) with the ANOVA results.

According to the ANOVA test, (all the means are the same., at least one mean is different., all the means are different.) That means that the conclusions of the two tests are (not consistent., consistent.)

  

Explanation / Answer

here we use one-way anova and following information has been generated from the given data

(a) since the p-value of the model is less han alpha=0.01 so we fail the accept H0

the null hypothesis is H0: M1=M2=M3=M4=M5, and

alternate hypothesis H1: Not all Mj are equal (where j=1, 2, 3, 4, 5)

The test statistic is=15.55

p-value is <0.000

Since the test statistic F= 15.55 is greater than 1% level of siginificance F(0.01,3,16)=5.292 , we reject H0

and conclude that

There is sufficient evidence of a significant difference in the median distances traveled among the different designs.

b. A one-way ANOVA of the same data gives F =15.546 with p-value = 0.000.

Compare the results in (a) with the ANOVA results.

According to the ANOVA test, ( at least one mean is different.) That means that the conclusions of the two tests are (, consistent.)

Source DF Sum of Squares Mean Square F Value p-value Model 3 1277.33 425.777 15.55 <.0001 Error 16 438.202 27.3876 Corrected Total 19 1715.53 R-Square Coeff Var Root MSE output Mean 0.744568 2.38127 5.23332 219.77 Source DF Anova SS Mean Square F Value p-value design 3 1277.33 425.777 15.55 <.0001

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