A classic tale involves fourcarpooling students who missed a test and gave an ex

Question

A classic tale involves fourcarpooling students who missed a test and gave an excuse of a flattire. On a makeup test, the instructor asked the students toidentify the particular tire that went flat. If they really didn'thave a flat tire, would they be able to identify the same tire? Theauthor asked 41 other students to identify the tire they wouldselect. The results are listed in the following table (except forone student who selected the spare). Use a 0.05 significance levelto test the claim that the results fit a uniform distribution. Whatdoes the result suggest about the ability of the four students toselect the same tire when they really did not have a flat?

Tire                       Left front       Rightfront     Leftrear      Right rear

Numberselected       11                 15                  8                 6

The answer is below, please help withthe solution, thank you : )

Test stat x² =4.600. Crit valx²=7.815??7. Tech P= 0.2035. Students can not select the sametire.

Test stat x² =4.600. Crit valx²=7.815??7. Tech P= 0.2035. Students can not select the sametire.

Explanation / Answer

To determine whether the selection follows a uniform distribution,we need to determine first how many would be expected, underindependence to pick each tire. Since there were 40 students and 4tires to choose from (not counting the spare), we would expect 10to choose each one. We can now perform a Chi-Square test for goodness of fit by addingup the values (Observed - Expected)2 / Expected   for eachof the 4 tire. For the left front we get (11-10)2 / 10 =.10 For the right front we get (15-10)2/ 10 = 2.5 For the left rear we get    (8-10)2/ 10 =.40 For the right rear we get (6 - 10)2/ 10 = 1.6 We sum these up to get 4.60. Using a 5% significance and the Chi-Square table we see that thenumber is less than the critical value, we conclude the could notall pick the same tire and their answers were uniform.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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