Deck 12: Confidence Intervals for Means

Question 1

Find the sample size.
Top management at a large software company wishes to estimate the average number
Of hours its firm's professional employees volunteer in the local community. Based on
Past similar studies, the standard deviation was found to be 2.22 hours. If top
Management wants to estimate the average number of hours volunteered per month by
Their professional staff to within one hour with 99% confidence, how many randomly
Selected professional employees would they need to sample?

A) 19
B) 25
C) 54
D) 44
E) 33

Answer 1

E

Question 2

Find the confidence interval.
Insurance companies track life expectancy information to assist in determining the cost
Of life insurance policies. ABI Insurance randomly sampled 100 recently paid policies
And determined the average age of clients in this sample to be 77.7 years with a standard
Deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance
Policy holders is

A) 77.1 to 78.3 years
B) 76.87 to 80.33 years
C) 75.4 to 80 years
D) 74.1 to 81.3 years
E) 72.5 to 82.9 years

Answer 2

A

Question 3

Find correct t* values.
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on
Data collected from its automatic filling process, the amount of cheese inserted into the
Ravioli is normally distributed. To make sure that the automatic filling process is on
Target, quality control inspectors take a sample of 25 ravioli. The correct value of t* to
Construct a 99% confidence interval for the true mean amount of cheese filling is

A) 2.797
B) 1.711
C) 2.787
D) 2.060
E) 1.318

Answer 3

A

Question 4

Find the confidence interval.
Grandma Gertrude's Chocolates, a family owned business, has an opportunity to
Supply its product for distribution through a large coffee house chain. However, the
Coffee house chain has certain specifications regarding cacao content as it wishes to
Advertise the health benefits (antioxidants) of the chocolate products it sells. In order to
Determine the mean % cacao in its dark chocolate products, quality inspectors sample 36
Pieces. They find a sample mean of 55% with a standard deviation of 4%.
The 90% confidence interval for the true mean % cacao is

A) 53.87% to 56.13%.
B) 51% to 59%.
C) 53.33% to 56.67%.
D) 53.64% to 56.36%
E) 54.33% to 55.67%.

Question 5

Check conditions / assumptions of confidence intervals for means.
Which of the following is not an assumption and / or condition required for constructing
A confidence interval for the mean?

A) Randomization condition
B) Nearly Normal condition
C) Success / Failure condition
D) 10% condition
E) Independence assumption

Question 6

Interpret the confidence interval.
A large software development firm recently relocated its facilities. Top management is
Interested in fostering good relations with their new local community and has encouraged
Their professional employees to engage in local service activities. They wish to
Determine the average number of hours the firm's professionals volunteer per month.
They find the 95% confidence interval of 14.62 to 15.78. Which of the following is the
Correct interpretation?

A) We are 95% confident that the average number of hours per month volunteered by professionals employed with this firm is between 14.62 and 15.78.
B) 95% of all firm's professional employees volunteer between 14.62 and 15.78 hours per month.
C) The number of hours per month volunteered by the firm's professional employees is between 14.62 and 15.78 95% of the time.
D) All of the above.
E) None of the above.

Question 7

Find the sample size.
A manufacturer of cheese filled ravioli wants to make sure that its automatic filling
Process is on target. Based on a sample of 25 ravioli the mean weight of cheese filling is
Estimated to be 15 grams with a standard deviation of 1.5 grams. However, the quality
Control inspectors wish to estimate the mean weight of cheese filling more accurately so
That they can be 99% confident that it is within .25 grams of the true mean. How many
Ravioli should they sample?

A) 150
B) 543
C) 212
D) 410
E) 239

Question 8

Find the margin of error.
Grandma Gertrude's Chocolates, a family owned business, has an opportunity to
Supply its product for distribution through a large coffee house chain. However, the
Coffee house chain has certain specifications regarding cacao content as it wishes to
Advertise the health benefits (antioxidants) of the chocolate products it sells. In order to
Determine the mean % cacao in its dark chocolate products, quality inspectors sample 36
Pieces. They find a sample mean of 55% with a standard deviation of 4%.
What is the margin of error at 95% confidence?

A) 1.13%
B) 1.36%
C) 0.67%
D) 4%
E) 1.67%

Question 9

Find the standard error of the mean.
In a metal fabrication process, metal rods are produced to a specified target length of
15 feet. Suppose that the lengths are normally distributed. A quality control specialist
Collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and
A standard deviation of 0.65 feet. The standard error of the mean is

A) 0.65 ft.
B) 0.346 ft.
C) 0.1625 ft.
D) 0.0098 ft.
E) 1.625 ft.

Question 10

Find the confidence interval.
A large software development firm recently relocated its facilities. Top management is
Interested in fostering good relations with their new local community and has encouraged
Their professional employees to engage in local service activities. They wish to
Determine the average number of hours the firm's professionals volunteer per month. A
Random sample of 24 professionals yields a mean of 16.6 hours and a standard deviation
Of 2.22 hours. The 95% confidence interval is

A) 14.62 to 15.78 hours.
B) 14.38 to 18.82 hours.
C) 14.95 to 18.25 hours.
D) 15.66 to 17.54 hours.
E) 16.04 to 17.16 hours.

Question 11

Find the standard error of the mean.
A small business ships specialty homemade candies to anywhere in the world. Past
Records indicate that the weight of orders is normally distributed. Suppose a random
Sample of 16 orders is selected and each is weighed. The sample mean was found to be
110 grams with a standard deviation of 14 grams. The standard error of the mean is

A) 14 grams
B) 0.875 grams
C) .35 grams
D) 3.5 grams
E) 27.5 grams

Question 12

Find correct t* values.
Grandma Gertrude's Chocolates, a family owned business, has an opportunity to
Supply its product for distribution through a large coffee house chain. However, the
Coffee house chain has certain specifications regarding cacao content as it wishes to
Advertise the health benefits (antioxidants) of the chocolate products it sells. In order to
Determine the mean % cacao in its dark chocolate products, quality inspectors sample 36
Pieces. They find a sample mean of 55% with a standard deviation of 4%. The correct
Value of t* to construct a 90% confidence interval for the true mean % cacao is

A) 2.797
B) 1.711
C) 1.690
D) 2.030
E) 1.318

Question 13

Find the margin of error.
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on
Data collected from its automatic filling process, the amount of cheese inserted into the
Ravioli is normally distributed. To make sure that the automatic filling process is on
Target, quality control inspectors take a sample of 25 ravioli and measure the weight of
Cheese filling. They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams. What is the margin of error at 90% confidence?

A) 0.3 grams
B) 0.5133 grams
C) 0.8391 grams
D) 1.5 grams
E) 0.06 grams

Question 14

Grandma Gertrude's Chocolates, a family owned business, has an opportunity to
supply its product for distribution through a large coffee house chain. However, the
coffee house chain has certain specifications regarding cacao content as it wishes to
advertise the health benefits (antioxidants) of the chocolate products it sells. In order to
determine the mean % cacao in its dark chocolate products, quality inspectors sample 36
pieces. They find a sample mean of 55% with a standard deviation of 4%.
a. Describe the sampling distribution for the sample mean.
b. What is the standard error?
c. What is the margin of error for 90% confidence?
d. What is the margin of error for 95% confidence?
e. Based on the sample results, find the 90% confidence interval and interpret.
f. Based on the sample results, find the 95% confidence interval and interpret.
g. For a more accurate determination of the mean weight, the quality control inspectors
wish to estimate it within 1% with 95% confidence. How many pieces of dark chocolate
should they sample?

Question 15

Find the confidence interval.
A small business ships specialty homemade candies to anywhere in the world. Past
Records indicate that the weight of orders is normally distributed. Suppose a random
Sample of 16 orders is selected and each is weighed. The sample mean was found to be
110 grams with a standard deviation of 14 grams. The 90% confidence interval for the
True mean weight of orders is

A) 103.87 to 116.14 grams.
B) 86.046 to 133.954 grams.
C) 99.5 to 120.5 grams.
D) 102.55 to 117.45 grams.
E) 103.14 to 116.86 grams.

Question 16

Interpret the confidence interval.
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on
Data collected from its automatic filling process, the amount of cheese inserted into the
Ravioli is normally distributed. To make sure that the automatic filling process is on
Target, quality control inspectors take a sample of 25 ravioli and measure the weight of
Cheese filling. They find the 99% confidence interval of 14.16 to 15.84 grams. Which of
The following is the correct interpretation?

A) We are 99% confident that the mean weight of cheese filling in all ravioli made by this process is between 14.16 and 15.84 grams.
B) 99% of all ravioli made by this process will have cheese filling weights between 14.16 and 15.84 grams.
C) The weight of cheese filling in the ravioli is between 14.16 and 15.84 grams 99% of the time.
D) All of the above.
E) None of the above.

Question 17

Find the confidence interval.
In a metal fabrication process, metal rods are produced to a specified target length of
15 feet. Suppose that the lengths are normally distributed. A quality control specialist
Collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and
A standard deviation of 0.65 feet. The 95% confidence interval for the true mean length
Of rods produced by this process is

A) 14.544 to 15.056 ft.
B) 14.345 to 15.255 ft.
C) 13.912 to 15.688 ft.
D) 14.454 to 15.146 ft.
E) 13.834 to 15.766 ft.

Question 18

Find the sample size.
ABI Insurance wants to estimate the average life expectancy to within one year with
95% confidence. Previous studies have shown the mean age life expectancy of its clients
To be 78.6 with a standard deviation of 4.48 years. How many randomly selected
Recently paid policies would they need to sample to achieve the desired level of accuracy?

A) 98
B) 121
C) 54
D) 78
E) 83

Question 19

Describe t-distributions.
A small business ships specialty homemade candies to anywhere in the world. Past
Records indicate that the weight of orders is normally distributed. Suppose a random
Sample of 16 orders is selected and each is weighed. The sample mean was found to be
110 grams with a standard deviation of 14 grams. Which of the following statements is
True?

A) The sampling distribution for the sample mean follows the t-distribution with 16 degrees of freedom.
B) The sampling distribution for the sample mean follows the t-distribution with 15 degrees of freedom.
C) The mean of the sampling distribution for the sample mean is 110 grams.
D) The sampling distribution for the sample mean is Normal with a mean of 110 grams and standard deviation of 14 grams.
E) The standard error is 14 grams.

Question 20

Describe t-distributions.
In a metal fabrication process, metal rods are produced to a specified target length of
15 feet. Suppose that the lengths are normally distributed. A quality control specialist
Collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and
A standard deviation of 0.65 feet. Which of the following statement is true?

A) The sampling distribution for the sample mean follows the t-distribution with 16 degrees of freedom.
B) The sampling distribution for the sample mean follows the t-distribution with 15 degrees of freedom.
C) The mean of the sampling distribution for the sample mean is 14.8 feet.
D) The sampling distribution for the sample mean is Normal with a mean of 14.8 feet and standard deviation of .65 feet.
E) The standard error is 0.65 feet.

Question 21

Find the sample size.
Grandma Gertrude's Chocolates, a family owned business, has an opportunity to
Supply its product for distribution through a large coffee house chain. However, the
Coffee house chain has certain specifications regarding cacao content as it wishes to
Advertise the health benefits (antioxidants) of the chocolate products it sells. Past data
Indicate a standard deviation of 4%. If quality control inspectors wish to estimate the %
Cacao to within 1% of the true mean with 95% confidence, how many pieces of
Chocolate should they sample?

A) 29
B) 62
C) 54
D) 89
E) 36