An article summarizes a report of law enforcement agencies regarding the use of social media to screen applicants for employment. The report was based on a survey of 726 law enforcement agencies. One question on the survey asked if the agency routinely reviewed applicant's social media activity during background checks. For purposes of this exercise, suppose that the 726 agencies were selected at random, and that you want to use the survey data to decide if there is convincing evidence that more than 25% of law enforcement agencies review applicants' social media activity as part of routine background checks.

(a)

The sampling distribution of p describes the behavior of p when random samples are selected from a particular population. Describe the shape, center, and spread of the sampling distribution of p for samples of size 726 if the null hypothesis

H₀: p = 0.25

is true. (Round your answers to three decimal places.)

The sampling distribution of p is ---Select--- approximately normal not approximately normal , and has mean

_p =

and standard deviation

_p = .

(b)

Would you be surprised to observe a sample proportion of p = 0.26 for a sample of size 726 if the null hypothesis

H₀: p = 0.25

is true? Explain why or why not.

Yes, it would be surprising since the probability is not particularly small.Yes, It would be very surprising since this probability is extremely small. No, it would not surprising since the probability is not particularly small.No, It would not be very surprising since this probability is extremely small.

(c)

Would you be surprised to observe a sample proportion of p = 0.32 for a sample of size 726 if the null hypothesis

H₀: p = 0.25

is true? Explain why or why not.

No, It would not be very surprising since this probability is extremely small.Yes, It would be very surprising since this probability is extremely small. No, it would not surprising since the probability is not particularly small.Yes, it would be surprising since the probability is not particularly small.