Question

10. According to a recent study, taller women have a significantly higher risk of developing some form of cancer. The American Cancer Society reports that approximately 38% of all women develop some form of cancer in their lifetime. A long-term Canadian study was conducted involving 1250 tall women between the ages of 50 and 79, and 502 of them developed women who develop cancer is greater than 0.38? Perform a hypothesis test at significance level a = 0.01. Use the 'Classical approach, clearly showing what you are some form of cancer. Is there evidence to suggest that the proportion of taller doing.

Answer 1

1250, the number of favorable cases 0.4016, and the significance level is a The following information is provided: The sample size is N is X 502, and the sample proportion is p 502 1250 0.01 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho p 0.38 Ha p0.38 This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used (2) Rejection Region Based on the information provided, the significance level is a 0.01, and the critical value for a 2.33 right-tailed test is z The rejection region for this right-tailed test is R {z : z> 2.33} (3) Test Statistics The z-statistic is computed as follows: 0.4016 0.38 p-po - 1.573 VPo (1- po)/n V0.38(1-0.38)/1250 (4) Decision about the null hypothesis Since it is observed that z 1.573< ze 2.33, it is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p 0.0578, and since p concluded that the null hypothesis is not rejected 0.0578 0.01, it is (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is greater than po, at the a = 0.01 significance level.