MATH 302 Week 5 Quiz – Question and Answers

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MATH 302 Week 5 Quiz with Answers

Part 1 of 4 – Z-interval for Unknown Questions

  1. A researcher would like to estimate the proportion of all children that have been diagnosed with Autism Spectrum Disorder (ASD) in their county. They are using 97% confidence level and the CDC national estimate that 1 in 68 ? 0.0147 children are diagnosed with ASD. What sample size should the researcher use to get a margin of error to be within 1.5%? Round up to the nearest integer, do not include decimals.
  2. The population standard deviation for the height of college basketball players is 3.1 inches. If we want to estimate 99% confidence interval for the population mean height of these players with a 0.58 margin of error, how many randomly selected players must be surveyed? (Round up your answer to nearest whole number, do not include any decimals) 
  3. The population standard deviation for the height of college football players is 2.7 inches. If we want to estimate a 95% confidence interval for the population mean height of these players with a 0.65 margin of error, how many randomly selected players must be surveyed? (Round up your answer to nearest whole number, do not include any decimals)
  4. There is no prior information about the proportion of Americans who support Medicare-for-all in 2019. If we want to estimate 95% confidence interval for the true proportion of Americans who support Medicare-for-all in 2019 with a 0.175 margin of error, how many randomly selected Americans must be surveyed? Answer: (Round up your answer to nearest whole number, do not include any decimals)
  5. Suppose a marketing company wants to determine the current proportion of customers who click on ads on their smartphones. It was estimated that the current proportion of customers who click on ads on their smartphones is 0.65. How many customers should the company survey in order to be 94% confident that the margin of error is 0.22 for the confidence interval of true proportion of customers who click on ads on their smartphones? Answer: (Round up your answer to nearest whole number,do not include any decimals)
  6. A random sample of college basketball players had an average height of 67.45 inches. Based on this sample, (64.9, 69.2) found to be a 95% confidence interval for the population mean height of college basketball players. Select the correct answer to interpret this interval.
  7. There is no prior information about the proportion of Americans who support gun control in 2019. If we want to estimate 97% confidence interval for the true proportion of Americans who support gun control in 2019 with a 0.27 margin of error, how many randomly selected Americans must be surveyed? Answer: (Round up your answer to nearest whole number, do not include any decimals)
  8. In a random sample of 80 people, 52 consider themselves as baseball fans. Compute a 92% confidence interval for the true proportion of people consider themselves as baseball fans and fill in the blanks appropriately. We are 92% confident that the true proportion of people consider themselves as baseball fans is between  0.557 and 0.743 . 
  1. Suppose a marketing company wants to determine the current proportion of customers who click on ads on their smartphones. It was estimated that the current proportion of customers who click on ads on their smartphones is 0.45 based on a random sample of 150 customers. Compute a 98% confidence interval for the true proportion of customers who click on ads on their smartphones and fill in the blanks appropriately.  0.356 < p < 0.545 (round to 3 decimal places)
  2. In a random sample of 145 people, 112 said that they watched educational TV. Find the 93% confidence interval of the true proportion of people who watched educational TV.
  3. A random sample found that 30% of 150 Americans were satisfied with the gun control laws in 2018. Compute a 98% confidence interval for the true proportion of Americans who were satisfied with the gun control laws in 2018 Fill in the blanks appropriately. A 98% confidence interval for the true proportion of Americans who were satisfied with the gun control laws in 2018 is (  0.213 , 0.387 )

Part 3 of 4 – Confidence Interval Questions

  1. If everything else stays the same, the margin of error can be reduced by:
  2. Senior management of a consulting services firm is concerned about a growing decline in the firm’s weekly number of billable hours. The firm expects each professional employee to spend at least 40 hours per week on work. In an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. Rather than reviewing the records of all the firm’s full-time employees, the management randomly selected a sample of size 50 from the available frame. The sample mean and sample standard deviations were 46.4 and 7.2 hours, respectively. Construct a 97% confidence interval for the average of the number of hours this firm’s employees spend on work-related activities in a typical week. Place your LOWER limit, in hours, rounded to 1 decimal place, in the first blank. For example, 6.7 would be a legitimate entry.  43.8. Place your UPPER limit, in hours, rounded to 1 decimal place, in the second blank. For example, 12.3 would be a legitimate entry.
  3. A sample of 9 production managers with over 15 years of experience has an average salary of $71,000 and a sample standard deviation of $18,000.
  4. Which confidence level would give the narrowest margin of error?
  5. A marketing research consultant hired by Coca-Cola is interested in determining the proportion of customers who favor Coke over other soft drinks. A random sample of 400 consumers was selected from the market under investigation and showed that 53% favored Coca-Cola over other brands. Compute a 95% confidence interval for the true proportion of people who favor Coke.  Place your LOWER limit, rounded to 3 decimal places, in the first blank  0.481 . For example, 0.345 would be a legitimate entry.  Place your UPPER limit in the second blank 0.579 . For example, 0.456 would be a legitimate entry.  Make sure you include the 0 before the decimal.

Part 4 of 4 – T-interval for Unknown Questions

  1. A randomly selected sample of college basketball players has the following heights in inches.See Attached Excel for Data. Compute a 95% confidence interval for the population mean height of college basketball players based on this sample and fill in the blanks appropriately.
  1. A random sample of college football players had an average height of 66.5 inches. Based on this sample, (64.2, 67.1) found to be a 95% confidence interval for the population mean height of college football players. Select the correct answer to interpret this interval.
  2. A random sample of college football players had an average height of 67.5 inches. Based on this sample, (65.9, 69.0) was found to be a 92% confidence interval for the population mean height of college football players. Select the correct answer to interpret this interval.
  3. A tire manufacturer wants to estimate the average number of miles that may be driven in a tire of a certain type before the tire wears out. Assume the population is normally distributed. A random sample of tires is chosen and are driven until they wear out and the number of thousands of miles is recorded, find the 97% confidence interval using the sample data.