How often does work intrude during off hours? A survey of 1,000 office workers indicated that 53% of males and 41% of females had office intrusion while on vacation. Assume that the survey consisted of 500 males and 500 females. At the 0.05 level of significance, is there evidence of a difference in the proportion of males and females who experience office intrusions while on vacation?

a.Specify the null hypothesis and the alternative hypothesis. State whether you are using a one- or two-tailed test and explain your reasoning.

b.Determine the appropriate hypothesis test to this problem. Justify your answer

c.Conduct calculations by hand to compute the critical value and p-value of the test. Determine your decision using two methods,the rejection regionandthe p-value approach.

d.Use R to conduct the hypothesis test. Copy and paste the command and output generated by R.

e.Communicate the results of the test in "plain English" including the meaning of the p-value.