Math 221 – quizzes – week 5 homework

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 standard deviation of 3.54. What is the 95% confidence interval for the amount of time spent on administrative issues?

(19.24, 24.14)

(20.71, 22.67)

(20.93, 22.46)

(21.78, 22.60)

Question 2

If a confidence interval is given from 43.8 up to 62.0 and the mean is known to be 52.9, what is the maximum error?

9.1

43.8

18.2

4.6

Question 3 

If a shirt manufacturer wanted to make shirts that fit most individuals, what characteristics would be better?

wide confidence interval so shirts fit few individuals

wide confidence interval so shirts fit most individuals

narrow confidence interval so shirts fit most individuals

narrow confidence interval so shirts fit few individuals

Question 4 

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

large sample size

large mean

small sample size

small standard deviation

Question 5 

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

a large maximum error

a large sample size

a large standard deviation

a large mean

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?

Stop the line as it is close to the confidence interval

Keep the line operating as it is close to the confidence interval

Keep the line operating as it is outside the confidence interval

Stop the line as it is outside the confidence interval

Question 7 

In a sample of 65 temperature readings taken from the freezer of a restaurant, the mean is 31.9 degrees and the standard deviation is 2.7 degrees. What would be the 80% confidence interval for the temperatures in the freezer?

(31.36, 31.90)

(31.47, 32.33)

(29.20, 34.61)

(26.59, 37.38)

Question 8 

What is the 99% confidence interval for a sample of 36 seat belts that have a mean length of 85.6 inches long and a standard deviation of 2.5 inches?

(84.5, 86.7)

(84.4, 86.8)

(83.1, 88.1)

(80.6, 90.6)

Question 9 

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

Sample A as it has the smaller sample

Sample B as its sample is more disperse

Sample A as its sample is more disperse

Sample B as it has the smaller 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 children’s toys where imprecision is expected

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

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

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

Question 11

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 standard deviation of 4.3 in a normally distributed population.

73

71

70

72

Question 12 

Determine the minimum sample size required when you want to be 99% confident that the sample mean is within 0.50 units of the population mean. Assume a standard deviation of 1.4 in a normally distributed population.

52

31

53

30

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 standard deviation of 3.8 hours. Find the 95% confidence interval.

(9.1, 16.7)

(10.5, 15.3)

(11.1, 14.7)

(10.2, 15.6)

Question 14

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?

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

t distribution as the sample 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 standard deviation of 0.3 ounces. What would be the 90% confidence interval?

(19.75, 20.35)

(19.92, 20.18)

(19.89, 20.21)

(19.88, 20.22)

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 50.04 to 50.40. What conclusion can be made?

The supplier products have a higher mean than claimed

The supplier is less accurate than they claimed

The supplier products have a lower mean than claimed

The supplier is more 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 this estimate was based on a sample of 8 customers, what would be the 95% confidence interval?

(0.21, 3.00)

(0.00, 3.27)

(-0.40, 3.60)

(-0.07, 3.27)

Question 18

In a sample of 28 cups of coffee at the local coffee shop, the average temperature was 162.5 degrees with a standard deviation of 14.1 degrees. What would be the 95% confidence interval for the temperature of your cup of coffee?

(157.96, 167.04)

(157.03, 167.97)

(148.40, 176.60)

(158.12, 166.88)

Question 19 

In 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 due to using the z distribution

It would become narrower with fewer values

It would become wider due to using the t distribution

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

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 76.8 with a 95% 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 76.800 with a 99% confidence interval of 76.5 to 77.1