5. A company produces metal pipes of a standard length, and claims that the variance of...

5. A company produces metal pipes of a standard length, and claims that the variance of the length is 1.44 cm. One of its clients decide to test this claim by taking a sample of 25 pipes and checking their lengths. They found that the standard deviation of the sample is 2.4 cm. Does this undermine the company’s claim?

A. State the hypotheses

b. Find the calculated value of the test statistic

c. Find the critical value at α = 0.05

d. State your conclusion

Solutions

Expert Solution

The provided sample variance is s^2 = 5.76 and the sample size is given by n = 25

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

This corresponds to a two-tailed test, for which a Chi-Square test for one population variance will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the the rejection region for this two-tailed test is

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that = 96 > = 39.364 , it is then concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population variance 2σ2 is different than 1.44, at the 0.05 significance level.

orchestra answered 2 years ago

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