Question

8/15 points 11 Previous Answers IllowskyintroStati 8.HW.123.general. My Notes Ask Your Teacher A telephone poll of 1000 adult Americans was reported in a magazine. One of the questions asked was "What is the main problem facing the country? Suppose 24% answered "crime". We are interested the main problem. in the population proportion of adult Americans who feel that crime assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) NOTE: you are using a Student's t-distribution, you Part (a) Part (b) Which distribution should you use for this problem? (Round your answers to three decimal places.) PN Explain your choice. The binomial distribution should be used because the two outcomes are "crime is the main problem" and "crime is not the main problem." O The standard normal distribution should be used because we are interested in proportions and the sample size is large. O The standard normal distribution should be used because npq 10. O The Student's -distribution should be used because we do not know the standard deviation. population proportion. Correct! We use the standard normal distribution to create confidence intervals about O Part (c) population proportion of adult Americans who feel that crime Construct a 95 % confidence interval for t the main problem four decimal places.) (i) State the confidence interval. (Round your answers i) Sketch the graph Part (c) Construct a 95 % confidence interval for the population proportion of adult Americans who feel that crime is the main problem. four decimal places.) i) State the confidence interval. (Round your answers (i) Sketch the graph. CL= 95 0.025 0.025 2 2 (iii Calculate the error bound. (Round your answer to four decimal places.) Part (d) |Part (e) Additional Materials Section 8.1 Chap 8 Homework 6/13 points Previous Answers IllowskylntroStati 8.HW.119. Ask Your Teacher a recent survey of 1600 people, 65% feel that the president According doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable job NOTE you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) Part (b) Which distribution should you use for this problem? (Round your answers to four decimal places.) P-N ( Explain your choice sample size is large. The standard normal distribution should be used because we are interested in proportions and OThe standard normal distribution should be used because ong 10, which implies a large sample O The binomial distribution should be used because the two outcomes are "the president is doing a good job" and "the president is not doing a good job." O The Student's t-distribution should be used because we do not know the standard deviation. population proportion. Correct! We use the standard normal distribution to ereate confidence intervals about Part (c) Construct a 90 % confidence interval for the population proportion of people who feel the president doing an acceptable job four decimal places.) (i) State the confidence interval. (Round your answers (i) Sketch the graph C.L= 90 0.05 0.05 Chap 8 Homework E Part (c) Construct a 90 % confidence interval for the population proportion of people who feel the president is doing an acceptable job. ) State the confidence interval. (Round your answers four decimal places.) (ii) Sketch the graph. C.L = 90 0.05 0,05 2 (ii) Calculate the error bound. (Round your answer to four decimal places.) Additional Materials E Section 8.1 812

Answer 1

Solution:-

1)

b)

The distribution we should use for the problem is Normal P $\sim$ N (240, 13.506)

np LL

1000 0.24

240

n* p(1 -p)

/1000 0.24(1- 0.24)

=13.506

The standard normal distribution should be used because we are interested in proportions and sample size is large.

c)

i) 95% confidence interval for the population proportion of adult american who feel that crime is the main problem is C.I = ( 0.2135, 0.2665).

C.I pt2a/2x 1/P(1-p)

C.I = 0.24 + 1.96 × 0.013506

C.I = 0.24 + 0.02647

C.I = ( 0.2135, 0.2665)

ii)

C.L=95 0.025 0.025 2 2 P' 1.96 1.96 (0.2135 0.2665) 8 N

iii) The error bound is + 0.0265

p(1- р) = tza/2 X п

M.E= + 1.96 × 0.013506

M.E = + 0.02647