Chapter 11: Confidence Intervals and Hypothesis Tests for Means – Quiz A
Name ________________________________________
11.3.3 Calculate and describe the standard error of the mean.
1. 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.
a. Describe the sampling distribution for the sample mean.
b. What is the standard error?
c. For 95% confidence, what is the margin of error?
d. Based on the sample results, create the 95% confidence interval and interpret.
11.5.6 Create and interpret confidence intervals for the mean.
2. 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.
a. Describe the sampling distribution for the sample mean.
b. What is the standard error?
c. What is the margin of error for 99% confidence?
d. What is the margin of error for 90% confidence?
e. Based on the sample results, find the 99% confidence interval and interpret.
f. Based on the sample results, find the 90% confidence interval and interpret.
g. For a more accurate determination of the mean weight, the quality control inspectors
wish to estimate it within 0.25 grams with 99% confidence. How many ravioli should
they sample?
11-2 Chapter 11 Confidence Intervals and Hypothesis Tests for Means
11.5.6 Create and interpret confidence intervals for the mean.
3. Insurance companies track life expectancy information to assist in determining the
cost of life insurance policies. Last year the average life expectancy of all policyholders
was 77 years. ABI Insurance wants to determine if their clients now have a longer life
expectancy, on average, so they randomly sample some of their recently paid policies.
The ages of the clients in the sample are shown below.
86 75 83 84 81 77 78 79 79 81
76 85 70 76 79 81 73 74 72 83
a. Based on the sample results, find the 90% confidence interval and interpret.
b. For more accurate cost determination, ABI Insurance wants to estimate the average life
expectancy to within one year with 95% confidence. How many randomly selected
recently paid policies would they need to sample?
c. Suppose ABI samples 100 recently paid policies. This sample yields a mean of 77.7
years and a standard deviation of 3.6 years. Find a 90% confidence interval and interpret.
11.5.6 Create and interpret confidence intervals for the mean.
4. A sample of students from an introductory business course were polled regarding the
number of hours they spent studying for the last exam. All students anonymously
submitted the number of hours on a 3 by 5 card. There were 24 individuals in the one
section of the course polled. The data was used to make inferences regarding the other
students taking the course. The data are shown below:
4.5 22 7 14.5 9 9 3.5 8 11 7.5 18 20
7.5 9 10.5 15 19 2.5 5 9 8.5 14 20 8
a. Based on the sample results, find the 95% confidence interval.
b. Interpret the results.
c. Do you expect a 90% confidence interval to be wider or narrower and why?
d. A previous study of a large cross-section of students in this course showed that
students studies 12 hours per week. Are the results of this current study statistically
different than the assumption of 12 hours per week studying? Define the hypotheses and
compare the t-value to the critical t value, evaluating at α = 0.05.
Quiz A 11-3
Chapter 11: Confidence Intervals and Hypothesis Tests for Means – Quiz A – Key
11-4 Chapter 11 Confidence Intervals and Hypothesis Tests for Means
Quiz A 11-5
11-6 Chapter 11 Confidence Intervals and Hypothesis Tests for Means
Quiz B 11-7
Chapter 11: Confidence Intervals and Hypothesis Tests for Means – Quiz B
Name ________________________________________
11.3.3 Calculate and describe the standard error of the mean.
1. 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.
a. Describe the sampling distribution for the sample mean.
b. What is the standard error?
c. For 90% confidence, what is the margin of error?
d. Based on the sample results, create the 90% confidence interval and interpret.
11.5.6 Create and interpret confidence intervals for the mean.
2. 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?
11-8 Chapter 11 Confidence Intervals and Hypothesis Tests for Means
11.5.6 Create and interpret confidence intervals for the mean.
3. 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 reported the following number of hours:
12 13 14 14 15 15 15 16 16 16 16 16
17 17 17 18 18 18 18 19 19 19 20 21
a. Based on the sample results, find the 95% confidence interval and interpret.
b. For a more accurate determination, 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?
c. Suppose 40 professional employees are randomly selected. This sample yields a mean
of 15.2 hours and a standard deviation of 1.8 hours. Find a 95% confidence interval and
interpret.
11.7.8 Perform hypothesis tests for means.
4. A pharmaceutical company wants to answer the question whether it takes longer than
45 seconds for a drug in pill form to dissolve in the gastric juices of the stomach.
A sample was taken from patients taken the given drug in pill form and times for the pills
to be dissolved were measured as the following:
42.7 43.4 44.6 45.1 45.6 45.9 46.8 47.6
a. State the hypotheses to test this question.
b. State the assumptions of the test.
c. Perform the test and determine if it is statistically significant at α= 0.05.
d. Interpret the result.
Quiz B 11-9
Chapter 11: Confidence Intervals and Hypothesis Tests for Means – Quiz B – Key
11-10 Chapter 11 Confidence Intervals and Hypothesis Tests for Means
Quiz B 11-11