13. The proportion of adult women in a certain geographical region is approximat

Question

13. The proportion of adult women in a certain geographical region is approximately 51%. A marketing survey telephones 500 people at random. Complete parts a through e below. a) What is the sampling distribution of the observed proportion that are women? O A. Approximately Exponential O B. Approximately Uniform O C. Approximately Normal O D. None of these b) What is the standard deviation of that proportion? (Round to four decimal places as needed.) c) Would you be surprised to find 53% women in a sample size of 500? O A. That is surprising because 0.53 is less than one standard deviation above mean. O B. That is surprising because 0.53 is more than two standard deviations above mean. O C. That is not surprising because 0.53 is more than one standard deviation above mean. O D. That is not surprising because 0.53 is less than one standard deviation above the mean. d) Would you be surprised to find 41% women in a sample size of 500? O A. That is surprising because 0.41 is less than two standard deviations below the mean. O B. That is not surprising because 0.41 is less than two standard deviations below the mean. O C. That is surprising because 0.41 is more than three standard deviations below the mean. O D. That is not surprising because 0.41 is more than three standard deviations below the mean.

Explanation / Answer

Q.13 Proprtion of adult women = 51% = 0.51

(a) sampling distribution of observed proportion are approximately normal. (Option C)

(b) Standard deviation of the proportion. SE = sqrt [p(1-p) /N] = sqrt [ 0.51 * 0.49/ 500] = 0.02236

(c) FOr one standard deviation away = p^ + se = 0.51 + 0.02236 = 0.53236 which is more than 53% so it is not unusual because 0.53 is less than one standard deviation above the population mean. (option D)

(d) FOr two standard deviation below = p^ - 2 * se = 0.51 - 2 * 0.02236 = 0.4653 > 0.41 so it is surprising because 0.41 is less than the two standard deviations below the mean.

(e) Here 195 women in the sample means that proportion of women are 195/500 = 39% = 0.39 so yes it will be surprising since 195 women represents a proportion of 39% , which is less than three standard deviation below the mean. (Option A)

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.