PLEASE PAY CLOSE ATTENTION TO WHAT IS BEING ASKED IN QUESTIONS. I have arrange the questions 1-6, please only provide answer with question number and part (ex. 1a, 1b, 2a, 2b, etc.). No explanation needed. I got two different sections so please categorize them by section please on top is 7.5 and bottom is 7.6.

Section 7.5 1.

A population has a mean of 400 and a standard deviation of 80. Suppose a simple random sample of size 100 is selected and E is used to estimate u. Use 2 table. a. What is the probability that the sample mean will be within :l:9 of the population mean (to 4 decimals)? b. What is the probability that the sample mean will be within :l:10 of the population mean (to 4 decimals)? Hint(s) Check My Work Suppose a random sample of size 47 is selected from a population with tr = 11. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). 3. The population size is infinite (to 2 decimals). b. The population size is N = 50,000 (to 2 decimals). c. The population size is N : 5000 (to 2 decimals). d. The population size is N = 500 (to 2 decimals). Hint(s) Check My Work In the EAI sampling problem, the population mean is $71,100 and the population standard deviation is $5000. For n = 30, there is a 0.4908 probability of obtaining a sample mean within :l:$600 of the population mean. Use ztable. a. What is the probability that E is within $600 of the population mean if a sample of size 60 is used (to 4 decimals)? b. Answer part (a) for a sample of size 120 (to 4 decimals). Barron's reported that the average number of weeks an individual is unemployed is 16.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 16.5 weeks and that the population standard deviation is 4.5 weeks. Suppose you would like to select a random sample of 45 unemployed individuals for a follow-up study. Use z-table. a. Show the sampling distribution of E, the sample mean average for a sample of 45 unemployed individuals. til A HI v II (to 1 decimal) a; = (to 4 decimals) Choose the correct graph. A. B. 13.2 13.6 14 14.4 14.8 15.2 15.6 16 16.4 16.8 17.2 17.6 18 18.4 18.8 19.2 XC. + + 30 30.4 30.8 31.2 31.6 32 32.4 32.8 33.2 33.6 34 34.4 34.8 35.2 35.6 36 X18.2 13.6 14 14.4 14.8 15.2 15.6 16 16.4 16.8 17.2 17.6 18 18.4 18.8 19.2 - Select your answer - V b. What is the probability that a simple random sample of 45 unemployed individuals will provide a sample mean within 1 week of the population mean? (to 4 decimals) 1 c. What is the probability that a simple random sample of 45 unemployed individuals will provide a sample mean within a week of the population mean? (to 4 decimals) According to the Current Results website, the state of California has a mean annual rainfall of 25 inches, whereas the state of New York has a mean annual rainfall of 47 inches. Assume that the standard deviation for both states is 2 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. Use ztable. a. Show the probability distribution of the sample mean annual rainfall for California. This is a normal probability distribution with E) = and gm 2 (to 4 decimals). b. What is the probability that the sample mean is within 1 inch of the population mean for California? (to 4 decimals) c. What is the probability that the sample mean is within 1 inch of the population mean for New York? (to 4 decimals) d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why? The probability of being within 1 inch is greater because the sample size is . Hint(s) Check My Work The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100. Use ztable. Round your answers to four decimal places. a. What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean? b. What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean? c. What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean? d. Which, if any, of the sample sizes in parts (a), (b), and (c) would you recommend to have at least a 0.95 probability that the sample mean is within $16 of the population mean? - Select your answer - VI Hint(s) Check My Work After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $26,750. Assume the population standard deviation is $7,400. Suppose that a random sample of 50 USC students will be taken from this population. Use ztable. a. What is the value of the standard error of the mean? (to nearest whole number) b. What is the probability that the sample mean will be more than $26,750? (to 2 decimals) c. What is the probability that the sample mean will be within $1,000 of the population mean? (to 4 decimals) d. How would the probability in part (c) change if the sample size were increased to 160? (to 4 decimals) Hint(s) Check My Work A researcher reports survey results by stating that the standard error of the mean is 35. The population standard deviation is 420. Use ztable. a. How large was the sample used in this survey? b. What is the probability that the point estimate was within :l:30 of the population mean? (to 4 decimals) Hint(s) Check My Work A random sample of size 100 is selected from a population with p = 0.40. a. What is the expected value of 1) (to 2 decimals)? b. What is the standard error 0pr (to 4 decimals)? c. Show the sampling distribution off). 0'; = (to 4 decimals) EH?) 2 (to 2 decimals) d. What does the sampling distribution of 13 show? - Select your answer - v Hint(s) Check My Work A population proportion is 0.20. A random sample of size 250 will be taken and the sample proportion i will be used to estimate the population proportion. Use the ztable. Round your answers to four decimal places. a. What is the probability that the sample proportion will be within ::0.03 of the population proportion? b. What is the probability that the sample proportion will be within :l:0.07 of the population proportion? Assume that the population proportion is 0.55. Compute the standard error of the proportion, 05, for sample sizes of 100, 200, 500, and 1000 (to 4 decimals). n = 100 n = 200 n = 500 n = 1000 What can you say about the size of the standard error of the proportion as the sample size is increased? ' - Select your answer - v The population proportion is 0.40. What is the probability that a sample proportion will be within :l:0.04 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places. Use ztable. 3'71 = 100 b'n = 200 C- n = 500 d'n = 1000 e. What is the advantage of a larger sample size? With a larger sample, there is a probability 5 will be within :l:0.04 of the population proportion p. Hint(s) Check My Work The president of Doerman Distributors, Inc., believes that 26% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of firsttime customers. Use ztable. a. Assume that the president is correct and p = 0.26. What is the sampling distribution 0pr for this study? - Select your answer - V, b. What is the probability that the sample proportion will be between 0.12 and 0.40 (to 4 decimals)? c. What is the probability that the sample proportion will be between 0.17 and 0.35 (to 4 decimals)? In 2016 the Better Business Bureau settled 85% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.85, the same as the overall proportion of complaints settled in 2016. Use the ztable. 3. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of 17. E0?) = (to 2 decimals) a; = (to 4 decimals) b. Based upon a sample of 200 complaints, what is the probability that the sample proportion will be within 0.01 of the population proportion (to 4 decimals)? probability = c. Suppose you select a sample of 400 complaints involving new car dealers. Show the sampling distribution of 5. E0?) = (to 2 decimals) a; = (to 4 decimals) d. Based upon the larger sample of 400 complaints, what is the probability that the sample proportion will be within 0.01 of the population proportion (to 4 decimals)? probability = e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (d)? The probability of the sample proportion being within 0.01 of the population mean is increased by (to 3 decimals). There is a gain in precision by - Select your answer - v the sample size. Hint(s) Check My Work The Grocery Manufacturers of America reported that 73.00% of consumers read the ingredients listed on a product's label. Assume the population proportion is p = 0.73 and a sample of 350 consumers is selected from the population. a. Show the sampling distribution of the sample proportion 5, where 5 is the proportion of the sampled consumers who read the ingredients listed on a product's label. EC?) 2 (to 2 decimals) a; = (to 4 decimals) b. What is the probability that the sample proportion will be within :l:0.03 of the population proportion (to 4 decimals)? c. Answer part (b) for a sample of 760 (to 4 decimals). The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.17 and a simple random sample of 800 households will be selected from the population. Use the ztable. a. Show the sampling distribution of 13, the sample proportion of households spending more than $100 per week on groceries. E(;r_1) = (to 2 decimals) 05 = (to 4 decimals) b. What is the probability that the sample proportion will be within :l:0.02 of the population proportion (to 4 decimals)? c. Answer part (b) for a sample of 1600 households (to 4 decimals). A market research rm conducts telephone surveys with a 38% historical response rate. What is the probability that in a new sample of 400 telephone numbers at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150 m = 0.375? Calculate the probability to 4 decimals. Use z-table. Hint(s) Check My Work The proportion of individuals insured by the AllDriver Automobile Insurance Company who received at least one traffic ticket during a fiveyear period is 0.15. Use the ztable. a. Show the sampling distribution of 13 if a random sample of 150 insured individuals is used to estimate the proportion having received at least one ticket. E(;T1) = (to 2 decimals) 05 = (to 4 decimals) Can the sampling distribution of}? be approximated by a normal distribution? - Select your answer - V b. What is the probability that the sample proportion will be within :|:0.03 of the population proportion (to 4 decimals)? Round zvalue to 2 decimals. Lori Jeffrey is a successful sales representative for a major publisher of college textbooks. Historically, Lori obtains a book adoption on 28% of her sales calls. Viewing her sales calls for one month as a sample of all possible sales calls, assume that a statistical analysis of the data yields a standard error of the proportion of 0.0600. Use the z-table. a. How large was the sample used in this analysis? That is, how many sales calls did Lori make during the month? b. Let 5 indicate the sample proportion of book adoptions obtained during the month. Show the sampling distribution off). The sampling distribution normal because up and n(1 p) are both 5. Choose the correct graph. A. .i..n....i...i...+_...............i. 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0.44 0.48 0.52 X - Select your answer - v c. Using the sampling distribution of i, compute the probability that Lori will obtain book adoptions on 32% or more of her sales calls during a onemonth period. (to 4 decimals)