MATH 221 Week 5 Quiz 1

MATH 221 Week 5 Quiz 1 | Devry University

Question 1

From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 21.69 with a population standard deviation of 3.54. What is the 95% confidence interval for the amount of time spent on administrative issues?

5VA. Confidence intervals with population standard deviation (Links to an external site.) (1:42)

5DA. Concept and meaning of confidence intervals (Links to an external site.) (DOCX)  

·         (20.71, 22.67)  

·         (20.93, 22.46)  

·         (20.78, 22.60)  

·         (19.24, 24.14)

 

 Question 2

If a confidence interval is given from 43.83 up to 61.97 and the mean is known to be 52.90, what is the margin of error?

5DB. Finding margin of error from given confidence interval (Links to an external site.) (DOCX)  

·         43.83  

·         4.54    

·         9.07  

·         18.14

 

Question 3

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

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)  

·         narrow confidence interval at high confidence level  

·         narrow confidence interval at low confidence level  

·         wide confidence interval with low confidence level  

·         wide confidence interval with high confidence level

 

 Question 4

The 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 56.99. What should be done about the production line?

5DE. Given a confidence interval and sample mean, what decisions can be made (Links to an external site.)(DOCX)  

·         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 inside the confidence interval  

·         Keep the line operating as it is outside the confidence interval

 

 Question 5

In a sample of 41 temperature readings taken from the freezer of a restaurant, the mean is 31.9 degrees and the population standard deviation is 2.7 degrees. What would be the 80% confidence interval for the temperatures in the freezer?

5VA. Confidence intervals with population standard deviation (Links to an external site.) (1:42)      

·         (31.36, 32.44)  

·         (31.36, 31.90)  

·         (31.90, 32.44)

 

 

Question 6

What 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?

 5VA. Confidence intervals with population standard deviation (Links to an external site.) (1:42)  

·         (83.1, 88.1)    

·         (84.6, 86.6)  

·         (84.4, 86.8)  

·         (84.7, 86.5)

 

Question 7

If two samples A and B had the same mean and sample size, but sample A had a larger standard deviation, which sample would have the wider 95% confidence interval?5DD. Changes in confidence interval based on changes in standard deviation or sample size (Links to an external site.) (DOCX)

  

·         Sample A as its sample is more disperse  

·         Sample A as it has the larger sample  

·         Sample B as it has the smaller sample  

·         Sample B as its sample is more disperse

 

 Question 8

Determine 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.

5VB. Calculating minimum sample size (Links to an external site.) (1:52)

5DG. Why set a minimum sample size (DOCX)  

·         55  

·         59    

·         56  

·         60

 

 Question 9

In 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.

5VE. Confidence intervals with sample standard deviation (Links to an external site.) (1:37)  

·         (9.1, 16.7)  

·         (10.2, 15.6)  

·         (10.5, 15.3)  

·         (11.1, 14.7)

 

 Question 10

In 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?

5VC. Using z or t  (Links to an external site.) (2:13)  

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

·         z distribution as the sample standard deviation always represents the population  

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

·         t distribution as the sample standard deviation is unknown

 

 Question 11

Under a time crunch, you only have time to take a sample of 15 water bottles and measure their contents. The sample had a mean of 20.05 ounces with a sample standard deviation of 0.3 ounces. What would be the 90% confidence interval, when we assumed these measurements are normally distributed?

5VE. Confidence intervals with sample standard deviation (Links to an external site.) (1:37)  

·         (19.91, 20.19)  

·         (19.92, 20.18)  

·         (19.75, 20.35)  

·         (19.88, 20.22)

 

 Question 12

Say 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 50.04 to 50.40. What conclusion can be made?

5VD. Comparing sample confidence intervals with given intervals (Links to an external site.) (3:43)

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)  

·         The supplier products have a lower mean than claimed  

·         The supplier is less accurate than they claimed  

·         The supplier products have a higher mean than claimed  

·         The supplier is more accurate than they claimed

 

 Question 13

In a sample of 28 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?

5VE. Confidence intervals with sample standard deviation (Links to an external site.) (1:37)  

·         (157.96, 167.04)  

·         (148.40, 176.60)  

·         (158.12, 166.88)   

·         (157.03, 167.97)

 

 Question 14

In a situation where the sample size was 28 while the population standard deviation was increased, what would be the impact on the confidence interval?

5DD. Changes in confidence interval based on changes in standard deviation or sample size (Links to an external site.) (DOCX)  

·         It would become wider due to using the z distribution  

·         It would become narrower due to using the t distribution  

·         It would widen with more values   

·         It would become wider with more dispersion in values

 

Question 15

You 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?

5DC. Confidence intervals in manufacturing, high vs low level of confidence, wide vs narrow (Links to an external site.) (DOCX)

5DF. Why companies in different industries use different levels of confidence (Links to an external site.) (DOCX)  

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

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

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

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