Statıstıcs Iı Deneme Sınavı Sorusu #993497
Assume that there are two different brands (A and B) producing chocolates. The variance of chocolates are assumed to be different. One chooses 10 chococaltes of brand A and 20 chocolates of brand B and observes that the average weight of brand A sample is 56 gr and brand B is 54 gr. The sample variances for A and B are 1 and 2 gr respectively. What will be the t-statistic and can we conclude that the weights of these brands are different at 0.05 significance level?
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t=1.65, weight are same |
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t=1.81, weights are same |
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t=2.98, weights are different |
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t=3.34, weights are same |
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t=4.47, weights are different |
so t=(56-54)/?(1/10+2/20)=2/?0.2=4.47. Degrees of freedom is 9 (since the smaller of 10-1 and 20-1 is 9) since the population variances are different. Thus the critical value of t=1.833. Since the calculated t is bigger than critical value we reject the null hypothesis that brand A and B have same weight. Thus we conclude that their weights differ at 0.05 significance level.
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