QA 233 (Basic Business Statistics)

Practice Problems VIII - Chapters 7 & 8


Hello QA 233 students! The following problems require you to use material from 'Sampling Distributions & Sampling' and 'Interval Estimation'  (slide sets 7 - 8 and chapters 7 & 8 in the ASW textbook). I have also posted the solutions on the Virtual Classroom web page. Have a good day.


  1. When surveyed, 41 out of 200 respondents indicate that ‘Twinkies’ are their favorite snack food. Provide both a point estimate and an interval estimate (at the 92% level of confidence) of the share of the population for whom ‘Twinkies’ are their favorite snack food. At the 90% level of confidence, what is the margin of error?
 
  1. Suppose that the mean sales for nineteen randomly selected restaurants in the ‘Hamburger Haven’ chain (which consists of 800 restaurants) during the week of the Thanksgiving holiday are $9,250.00. If the standard deviation of these sample results is $1250.00, what is the 95% confidence interval?
 
  1. Suppose that the mean sales for nineteen randomly selected restaurants in the ‘Hamburger Haven’ chain (which consists of 800 restaurants) during the week of the Thanksgiving holiday are $9,250.00. If the standard deviation of these sample results is $1250.00 and mean weekly sales for restaurants in the ‘Hamburger Haven’ chain tends to be normally distributed, what is the 95% confidence interval?
 
  1. If the actual mean weekly sales restaurants in the ‘Hamburger Haven’ chain is $11,200.50 and the actual standard deviation of weekly sales for restaurants in the ‘Hamburger Haven’ chain is $2,898.43, what is the probability that a randomly selected sample of 43 restaurants in the ‘Hamburger Haven’ will yield a mean of $12,500.00 or greater? Under these conditions, what is the probability that a randomly selected sample of 43 restaurants in the ‘Hamburger Haven’ will yield a mean between $12,000.00 and $12,230.00?
 
  1. If 5% of all output produced by a machine is defective, what is the probability that the proportion of defectives in the output produced by the machine today (300 units) is between .04 and .07? If our policy is perform maintenance on the machine when the proportion of defects in one day’s production exceeds 0.06, what is the probability that we will have to call maintenance at the end of any day? Given your results, what do you think of their maintenance policy (to perform maintenance on the machine when the proportion of defects in one day’s production exceeds 0.06)?
 
  1. Suppose that the mean checking account balance at a local bank is $750.00, and the standard deviation of checking account balances at the local bank is $500.00. Construct an interval that will contain 90% of all possible sample mean checking account balances that can result from a random sample of 45 checking accounts taken from the local bank.
 
  1. Farmer Douglass, who has an orchard of 2,000 pomegranate trees, wants to estimate the proportion of trees whose fruit are ripe. He and his able bodied assistant Eb randomly select 35 trees and determine that the fruit of 19 of the sampled trees is ripe. Farmer Douglass now wants an interval estimate, at the 99% confidence level, of the proportion of trees in his orchard whose fruit are ripe. Please provide farmer Douglass with this estimate. Do you think that this interval estimate will be useful to farmer Douglass? Why or why not?
 
  1. Suppose that 82% of all investors in the bond market earned a profit during the past fiscal year. Local bond dealer E. Z. Cash has seventy investors in the bond market, fifty of whom earned a profit during the past fiscal year. If we randomly select seventy investors, what is the probability the proportion of these investors who earned a profit during the past fiscal year would be at least as low as the proportion of E. Z.’s investors who earned a profit during the past fiscal year?
 
  1. A computer equipment manufacturer advertises that their 2500-L laser jet printer averages 12 printed pages per minute with a standard deviation of 1.50 pages per minute. You randomly select 50 documents from your hard drive and measure the number of pages printed in the first minute of printing for each document. The mean number of pages printed in the first minute for these 50 documents is 11.4. If the advertisement is accurate, what is the probability of getting results at least as poor as those you obtained (i.e., that the print speed is no more than 11.4 pages per minute for the first minute of printing for 50 randomly selected documents)?

 


 

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