The operations manager of a company that manufactures tires wants to determine whether there are any differences in the quality of work among the three daily shifts. She randomly selects 300 tires and carefully inspects them. Each tire is either classified as perfect, satisfactory, or defective, and the shift that produced it is also recorded. The two categorical variables of interest are "shift" and "condition of the tire produced". The p-value of the Chi-Squared test of independence is 0.073. Does the data provide sufficient evidence at the 5% significance level to infer that there are differences in quality among the three shifts?

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30-07-2021
Mathematics

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The operations manager of a company that manufactures tires wants to determine whether there are any differences in the quality of work among the three daily shifts. She randomly selects 300 tires and carefully inspects them. Each tire is either classified as perfect, satisfactory, or defective, and the shift that produced it is also recorded. The two categorical variables of interest are "shift" and "condition of the tire produced". The p-value of the Chi-Squared test of independence is 0.073. Does the data provide sufficient evidence at the 5% significance level to infer that there are differences in quality among the three shifts?

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Munali Munali · Answer 1 · 2021-08-07T08:53:22+02:00

The operation manager is responsible to identify whether there are errors in quality of the tires manufactured.

There are three different shifts and each shift has different team of workers who manufacture tires. For this we test hypothesis as;

H0 ; Quality of tire manufactured is independent on shifts

Ha ; Quality of tires manufactured is dependent on shifts.

The p value of chi squared test is greater than the significance level therefore we reject the null hypothesis.

This hypothesis reach to conclusion that quality of tires is dependent on shifts, which means there are differences in quality among the three shifts.

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