High-fiber food and cancer. According to research reported in the Journal of the National Cancer Institute (Apr. 1991), eating foods high in fiber may help protect against breast cancer. The researchers randomly divided 120 laboratory rats into four groups of 30 each. All of the rats were injected with a drug that causes breast cancer. Then each rat was fed a diet of fat and fiber for 15 weeks. However, the levels of fat and fiber varied from group to group. At the end of the feeding period, the number of rats with cancer tumors was determined for each group. The data are summarized in the table on p. 474.
a. Does the sampling appear to satisfy the assumptions for a multinomial experiment? Explain.
b. Calculate the expected cell counts for the contingency table.
c. Calculate the X2 statistic.
d. Is there evidence to indicate that diet and presence/ absence of cancer are independent? Test, using α = 05.
e. Compare the percentage of rats on a high-fat, no-fiber diet with cancer with the percentage of rats on a high-fat,
TUMORS
Diet | Totals | |||||
High Fat/No Fiber | High Fat/Fiber | Low Fat/No Fiber | Low Fat/Fiber | |||
Cancer Tumors | Yes | 27 | 20 | 19 | 14 | 80 |
No | 3 | 10 | 11 | 16 | 40 | |
Totals | 30 | 30 | 30 | 30 | 120 | |
Source: Tampa Tribune,Apr 3, 1991.
fiber diet with cancer, using a 95% confidence interval. Interpret the result.
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