Data set 16 in Appendix B lists the sugar content (grams of sugar per gram of cereal) for a sample of different cereals. Those amounts are summarized with these statistics: n= 16, xbar= 0.295, s= 0.168g. Use a 0.05 significance level to test the claim of a cereal lobbyist that the mean for all cereals is less than 0.3g.

Solution: We need to test the following hypotheses:

We use a t-test (the sample size is not big enough to use normal approximation), and we compute the t-statistics as:

The critical value for this left-tailed test is -1.753, which means that we cannot reject the null hypothesis. That implies that we don’t have enough evidence to support the claim that the mean for all cereals is less than 0.3g.

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