3 A researcher performs a hypothesis test at the alpha 005

3. A researcher performs a hypothesis test at the alpha = 0.05 level of significance. The null hypothesis is p = 0.85 and the alternative (or alternate) hypothesis is p not = to 0.85. The researcher uses the sample proportion and correctly calculates the test statistic to be z = 2.59 and the p-value to be 0.0096. Based on these results, the researcher correctly decides to reject the null hypothesis. (5 points) a... which statement correctly interprets the results of this hypothesis test? a) The researcher has proven that the population proportion is equal to 0.85. b) The re5earcher has proven that the population proportion is different from 085 c) Evidence suggests that the population proportion is 0.85. d) Evidence suggests that the population proportion is different from 0.85. b. Which one of the following correctly describes the type of error that the researcher may have committed in the hypothesis test described above? (5 points) a) The researcher may have rejected the null hypothesis when in reality the null hypothesis was true. b) The researcher may have rejected the null hypothesis when in reality the null hypothesis was false. c) The researcher may have rejected the null hypothesis when in reality the alternative hypothesis was false. c. What is the probability that the researcher committed an error by rejecting the null hypothesis? (5 points) a) O b) 0.05 c) 0.95 d) can?t be determined

Solution

a) (d) is correct interpretation as it is unlikely to have such a sample if true population mean was 0.85

b) both (a) and (c) are correct and represent type I error which might have occured in above conclusion

c) This is 0.05, same as the significance level given in question