# MATH221 Homework Week 5

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MATH221 Homework Week 5
From a random sample of 58 businesses, it is found that the mean time the owner spends…

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## MATH221 Homework Week 5

MATH221 Homework Week 5

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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 3.23. What is the 95% confidence interval for the amount of time spent on administrative issues?

(19.24, 24.14)

(21.78, 22.60)

(20.86, 22.52)

(20.71, 22.67)

Question 2

If a confidence interval is given from 43.85 up to 61.95 and the mean is known to be 52.90, what is the margin of error?

18.10

43.85

4.25

9.05

Question 3

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

narrow confidence interval at high confidence level

wide confidence interval with high confidence level

wide confidence interval with low confidence level

narrow confidence interval at low confidence level

Question 4

Which of the following are most likely to lead to a narrow confidence interval?

small sample size

large standard deviation

large mean

small standard deviation

Question 5

If you were designing a study that would benefit from very disperse data points, you would want the input variable to have:

a small standard deviation

a large mean

a large margin of error

a large sample size

Question 6

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 57.04. What should be done about the production line?

Keep the line operating as it is outside the confidence interval

Stop the line as it is outside the confidence interval

Keep the line operating as it is inside the confidence interval

Stop the line as it is inside the confidence interval

Question 7

In 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?

(27.00, 32.4)

(29.16, 30.24)

(24.30, 35.10)

(31.36, 32.44)

Question 8

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?

(84.7, 86.5)

(84.6, 86.6)

(83.1, 88.1)

(84.4, 86.8)

Question 9

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

Sample B as its sample is more dispersed

Sample A as it comes first

Sample B as it has the smaller sample

Sample A as it has the larger sample

Question 10

Why might a company use a lower confidence interval, such as 80%, rather than a high confidence interval, such as 99%?

They make computer parts where they are too small for higher accuracy

They make children’s toys where imprecision is expected

They are in the medical field, so cannot be so precise

They track the migration of fish where accuracy is not as important

Question 11

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

15

13

14

12

Question 12

Determine the minimum sample size required when you want to be 99% confident that the sample mean is within 0.25 units of the population mean. Assume a population standard deviation of 2.9 in a normally distributed population.

893

892

517

365

Question 13

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 4.9 hours. Find the 95% confidence interval. Assume the times are normally distributed.

(11.1, 14.7)

(9.4, 16.4)

(8.0, 17.8)

(9.9, 15.9)

Question 14

In a sample of 31 kids, their mean time on the internet on the phone was 36.5 hours with a sample standard deviation of 8.3 hours. Which distribution would be most appropriate to use, when we assume these times are normally distributed?

z distribution as the population standard deviation is known

z distribution as the sample standard deviation is known

t distribution as the sample standard deviation is unknown

t distribution as the population standard deviation is unknown

Question 15

Under 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)

(19.25, 20.85)

(19.63, 20.47)

(18.45, 21.65)

Question 16

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 50.00 to 50.36. What conclusion can be made?

The supplier is more accurate than they claimed

The supplier products have a lower mean than claimed

The supplier products have a higher mean than claimed

The supplier is less accurate than they claimed

Question 17

Market research indicates that a new product has the potential to make the company an additional \$1.6 million, with a standard deviation of \$2.0 million. If these estimates were based on a sample of 8 customers from a normally distributed data set, what would be the 95% confidence interval?

(0.00, 3.27)

(-0.40, 3.60)

(0.21, 3.00)

(-0.07, 3.27)

Question 18

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?

(157.03, 167.97)

(157.96, 167.04)

(148.40, 176.60)

(158.12, 166.88)

Question 19

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?

It would become wider with more dispersion in values

It would widen with more values

It would become narrower due to using the t distribution

It would become wider due to using the z distribution

Question 20

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?

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

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

MATH221 Homework Week 5

DeVry