Question

3. The local mob still wishes to purchase cement. As a result of an unfortunate misunderstanding, the Ace Cement Company (see problem 2) is no longer in business. Therefore, the mob asks the Nock Cement Company and the Out Cement Company to submit bids. Both companies offer their products at identical rock-bottom prices, and both products have equal average strength. Nock, however, claims its product is more reliable because the variability of its strength is less than that of its competitor's product. The mob then decides to make both companies an offer they can't refuse: the mob will take a random sample of 5 bags of cement from each firm, and test Nock's claim. The sample variance of Nock's product is found to be 10.4, while that of Out's product is found to be 14.7. Test Nock's claim at an alpha of 0.05.

Answer 1

The test of equality of variance can be performed through an F-test, where the F-statistics is defined as the ratio of the variance of the two samples and the degrees of freedoms are (n-1) and (m-1) for numerator and denominator, where n and m are the number of observations of sample 1 and sample 2 respectively.

In the present case, n = m = 5. The sample variance of Nock's product = 10.4 and that of Out's product = 14.7.

The null hypothesis can be stated as H₀: Variance_{Out's Product} > Variance_{Nock's Product} and the alternative hypothesis would be H₀: Variance_{Out's Product} <= Variance_{Nock's Product}

Hence, the F-statistic would be F = 14.7/10.4 = 1.413.

The critical value with degree of freedom (4,4) at 5% level of significance = 2.06 (one-tailed)

Since, the calculated F (i.e., 1.413) < the critical value (i.e., 2.03), the null hypothesis can not be rejected.

Hence, the conclusion is Variance_{Out's Product} > Variance_{Nock's Product}

In other words, the Nock's claim is correct at 5% level of significance.

cement from each firm, and test NOCN variance of Nock's product is found to be 10.4, while that Out's product is found to be 14.7. Test Nock's claim at an alpha of 0.05.