Devry MATH221 Week 5 Homework Latest 2021 June

MATH221 Statistics for Decision Making

Week 5 Homework

Question 1From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 20.53 with a population standard deviation of 3.54. What is the 95% confidence interval for the amount of time spent on administrative issues?

  (16.99, 24.07)

  (19.62, 21.44)

  (19.24, 24.14)

  (13.45, 27.61)

 Question 2If a confidence interval is given from 45.82 up to 55.90 and the mean is known to be 50.86, what is the margin of error?

  10.08

  2.52

  45.82

  5.04

 Question 3If a car manufacturer wanted lug nuts that fit nearly all the time, what characteristics would be better?

  wide confidence interval with low confidence level

  narrow confidence interval at high confidence level

  wide confidence interval with high confidence level

  narrow confidence interval at low confidence level

 Question 4The 95% confidence interval for these parts is 56.98 to 57.05 under normal operations. A systematic sample is taken from the manufacturing line to determine if the production process is still within acceptable levels. The mean of the sample is 57.04. What should be done about the production line?

  Stop the line as it is inside the confidence interval

  Stop the line as it is outside the confidence interval

  Keep the line operating as it is outside the confidence interval

  Keep the line operating as it is inside the confidence interval

 Question 5In a sample of 41 temperature readings taken from the freezer of a restaurant, the mean is 29.7 degrees and the population standard deviation is 2.7 degrees. What would be the 80% confidence interval for the temperatures in the freezer?

  (31.36, 32.44)

  (24.30, 35.10)

  (29.16, 30.24)

  (27.00, 32.4)

Question 6What is the 99% confidence interval for a sample of 52 seat belts that have a mean length of 85.6 inches long and a population standard deviation of 2.9 inches?

  (83.1, 88.1)

  (84.7, 86.5)

  (84.4, 86.8)

  (84.6, 86.6)

Question 7If two samples A and B had the same mean and standard deviation, but sample A had a smaller sample size, which sample would have the wider 95% confidence interval?

  Sample B as it has the larger sample

  Sample A as it comes first

  Sample A as it has the smaller sample

  Sample B as its sample is more disperse

 Question 8Determine the minimum sample size required when you want to be 95% confident that the sample mean is within one unit of the population mean. Assume a population standard deviation of 3.8 in a normally distributed population.

  60

  55

  56

  59

 Question 9In a sample of 10 CEOs, they spent an average of 12.9 hours each week looking into new product opportunities with a sample standard deviation of 3.8 hours. Find the 95% confidence interval. Assume the times are normally distributed.

  (11.1, 14.7)

  (10.5, 15.3)

  (10.2, 15.6)

  (9.1, 16.7)

 Question 10In a sample of 18 kids, their mean time on the internet on the phone was 28.6 hours with a sample standard deviation of 5.6 hours. Which distribution would be most appropriate to use, when we assume these times are normally distributed?

  z distribution as the sample standard deviation always represents the population

  t distribution as the sample standard deviation is unknown

  z distribution as the population standard deviation is known while the times are assumed to be normally distributed

  t distribution as the population standard deviation is unknown while the times are assumed to be normally distributed

Question 11Under a time crunch, you only have time to take a sample of 10 water bottles and measure their contents. The sample had a mean of 20.05 ounces with a sample standard deviation of 0.8 ounces. What would be the 90% confidence interval, when we assumed these measurements are normally distributed?

  (19.59, 20.51)

  (18.45, 21.65)

  (19.25, 20.85)

  (19.63, 20.47)

 Question 12Say that a supplier claims they are 99% confident that their products will be in the interval of 50.02 to 50.38. You take samples and find that the 99% confidence interval of what they are sending is 50.00 to 50.36. What conclusion can be made?

  The supplier products have a lower mean than claimed

  The supplier products have a higher mean than claimed

  The supplier is more accurate than they claimed

  The supplier is less accurate than they claimed

 Question 13In a sample of 20 cups of coffee at the local coffee shop, the temperatures were normally distributed with a mean of 162.5 degrees with a sample standard deviation of 14.1 degrees. What would be the 95% confidence interval for the temperature of your cup of coffee?

  (156.32, 168.68)

  (157.96, 167.04)

  (155.90, 169.10)

  (148.40, 176.60)

 Question 14In a situation where the sample size from a normally distributed data set was decreased from 45 to 22, what would be the impact on the confidence interval?

  It would become narrower with fewer values

  It would remain the same as sample size does not impact confidence intervals

  It would become wider due to using the t distribution

  It would become narrower due to using the z distribution

Question 15You needed a supplier that could provide parts as close to 76.8 inches in length as possible. You receive four contracts, each with a promised level of accuracy in the parts supplied. Which of these four would you be most likely to accept?

  Mean of 76.800 with a 90% confidence interval of 76.6 to 77.0

  Mean of 76.800 with a 99% confidence interval of 76.5 to 77.1

  Mean of 76.8 with a 95% confidence interval of 76.6 to 77.0

  Mean of 76.8 with a 99% confidence interval of 76.6 to 77.0