(a) What are the null and alternative hypotheses, and level of significance, for this hypothesis test?(b) What is the distribution of the test statistic for this hypothesis test? (2 marks) options below: -t3187 -N(3187, 0.89) -N(0, 1) -t3186 -Chi-square distribution with 4 degrees of freedom(c)What is the decision rule for this hypothesis test?(d)What is the observed test statistic for this hypothesis test? (2 marks)(d)What is the p-value for this hypothesis test?(e)What is the correct conclusion for this hypothesis test?(f)Suppose other researchers want to estimate p using a confidence interval. How many women do they need to sample, to estimate p to within 0.03 and with 90% confidence?

It is believed that 91% of women are right-handed. A study found that out of a random sample of 3187 men, 2868 of them were right-handed. Let p denote the proportion of men who are right-handed. Suppose we want to test, at the 1% level of significance, whether the proportion of men who are right-handed is not equal to the proportion of women who are right-handed. Assume the assumptions to this hypothesis test are satisfied. Answer the following questions