Question

OMG321 Business Statistics Prof Jian-yu Fisher Ke 2. We are interested in determining whether or not the variances of the sales at two small grocery stores are squal, A sample of sales at each store indicated the following. Store A n 10 S $130 Store B S $100 Are the variançes of the populations equal? Use a -00s.(15 points) a) Formulate the hypotheses.(S points) b) Calculate the test statistics (f value) and test the hypotheses. What is the eonclusion? (10 points)

Answer 1

a) H₀: $\sigma1^2 = \sigma2^2$

    H₁: $\sigma1^2 \neq \sigma2^2$

b) The test statistic F = s1^2/s2^2

                                  = (130)^2/(100)^2

                                  = 1.69

At alpha = 0.05, the critical values are F(0.025, 9, 7) = 0.2383

                                                             P(0.975, 9, 7) = 4.8232

Since the test statistic value lies between the critical values (0.2383 < 1.69 < 4.8232), so we should not reject the null hypothesis.

So at $\alpha$ = 0.05, we can conclude that the population variances are equal.