A researcher performs a hypothesis test at the a 005 level

A researcher performs a hypothesis test at the a = 0.05 level of significance. The null hypothesis is p = 0.85 and the alternative (or alternate) hypothesis is p ¹ 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.   

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 researcher has proven that the population proportion is different from 0.85.

                  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?

                  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?

                  a)              0

                  b)              0.05

                  c)              0.95

             d)   can’t be determined

Solution

a) option (D) is correct because p-value is less than 0.05, so we reject null and conclude (d)

b) Both (a) and (c) describe type-I error which might have happenend in above.

c) (b) 0.05 is correct (significance level)