Question

Many cheeses are produced in the shape of a wheel. Because of the differences in consistency between these different types of cheese, the amount of cheese, measured by weight, varies from wheel to wheel. Heidi Cembert wishes to determine whether there is a significant difference, at the 10% level, between the weight per wheel of Gouda and Brie cheese. She randomly samples 13 wheels of Gouda and finds the mean is 1.5 lb with a standard deviation of 0.31 lb; she then randomly samples 20 wheels of Brie and finds a mean of 1.03 lb and a standard deviation of 0.27 lb. What is the p-value for Heidi's hypothesis of equality? Assume normality. (Give your answer correct to four decimal places.)

Answer 1

The following null and alternative hypotheses need to be tested This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used (2) Rejection Region Based on the information provided, the significance level is a = 0.1, and the degrees of freedom are df-31. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal Hence it is found that the critical value for this two-tailed test is tc-1.696, for α 0.1 and df-31 The rejection region for this two-tailed test is R t 1.696 Since it is assumed that the population variances are equal, the t-statistic is computed as follows X1-X2 1.5 1.03 = 4.61 13-1)0.31201)0.27 (1 13+20-2 13 20 Since it is observed that4.61t1.696, it is then concluded that the null hypothesis is rejected Using the P-value approach: The p-value is p = 0.0001, and since P = 0.0001 < 0.1, it is 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 population mean μ1 is different than μ2, at the 0.1 significance level. Confidence Interval The 90% confidence interval is 0.297 < μ,-P2 < 0.643.