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MATH225 Week 6 Assignment: Confidence Interval
1. On a busy Sunday morning, a waitress randomly sampled customers about their preference for morning
beverages, Specifically, she wanted to find out how many people preferred coffee over tea. The proportion
of customers that preferred coffee was 0.42 with a margin of error 0.07.
Construct a confidence interval for the proportion of customers that preferred coffee.
2. A company sells juice in 1quart bottles. In a quality control test, the company found the mean volume of
juice in a random sample of bottles was X = 31 ounces, with a marginal error of 3 ounces.
Construct a confidence interval for the mean number of ounces of juice bottled by this company.
3. Randomly selected employees at an office were asked to take part in a survey about overtime. The office
manager wanted to find out how many employees worked overtime in the last week. The proportion of employees
that worked overtime was 0.83, with a margin of error of 0.11.
4. A random sample or garter snakes were measured, and the proportion of snakes that were longer than 20
inches in length recorded. The measurements resulted in a sample proportion of p = 0.25 with a sampling
standard deviation of Op = 0.05.
Write a 68% confidence interval for the true proportion of garter snakes that were over 20 inches in length.
5. The average number of onions needed to make French onion soup from the population of recipes is unknown.
A random sample of recipes yields a sample mean of x = 8.2 onions. Assume the sampling distribution of the
mean has a standard deviation of 2.3 onions.
Use the Empirical Rule to construct a 95% confidence interval for the true population mean number of onions.
Since 95% falls in 2 SD’s the calculation would be (8.2 – 4.6) “4.6 is the margin of error”, (8.2 + 4.6) = (3.6) , (12.8)
6. In a survey, a random sample of adults were asked whether a tomato is a fruit or vegetable. The survey
resulted in a sample proportion of 0.58 with a sampling standard deviation of 0.08 who stated a tomato is a fruit.
Write a 99.7 confidence interval for the true proportion of number of adults who stated the tomato is a fruit.
(0.58 – 3 x 0.08), (0.58 + 3 x 0.08) =(0.58 – .24), (0.58 + .24) = 0.34 + 0.
7. A college admissions director wishes to estimate the mean number of students currently enrolled. The age of
random sample of 23 students is given below. Assume the ages are approximately normally distributed. Use Excel
to construct a 90% confidence interval for the population mean age. Round your answer to 2 decimal places and
use increasing order.
Use week 6 worksheet to get mean and SD.
Data
25.8 Mean 23.
22.2 Sample Standard Deviation 1.
8. Suppose that the scores of bowlers in a particular league follow a normal distribution such that a standard
deviation of the population is 12. Find the 95% confidence interval of the mean score for all bowlers in this league
using the accompanying data set of 40 random scores. Round your answers to 2 decimal places using ascending
n 49 Mean 251. StDev 37. pop stdev yes SE 5. z 1. Margin of Error 10. Lower Limit 241. Upper Limit 262.
12. Suppose heights, in inches of orangutans are normally distributed and have a known population standard
deviation of 4 inches. A random sample of 16 orangutans is taken and gives a sample mean of 56 inches. Find the
confidence interval of the population mean with a 95% confidence level.
Lower limit = 54.04 and Upper Limit = 57.
13. The population standard deviation for the total snowfalls per year in a city is 13 inches. If we want to be 95%
confident that the sample mean is within 3 inches of the true population mean, what is the minimum sample size
that should be taken?
Answer: 73 snowfalls
Minimum Sample Size μ for population mean
Confidence Level 0. StDev 13 Error 3 z-Value 1. Minimum Sample Size 73
14. The population standard deviation for the body weights for employees of a company is 10 pounds. If we want
to be 95% confident that the sample mean is within 3 pounds of the true population mean, what is the minimum
sample size that should be taken.
Answer: 43 employees
Minimum Sample Size μ for population mean
Confidence Level 0. StDev 10 Error 3 z-Value 1. Minimum Sample Size 43
15. The length, in words, of the essays written for a contest are normally distributed with a population standard
deviation of 442 words and an unknown population mean. If random sample of 24 essays is taken and results in a
sample mean of 1330 words, find a 99% confidence interval for the population mean. Round to two decimal
places.
Answer: Lower limit = 1097.59 upper Limit = 1562.
16. Brenda wants to estimate the percentage of people who eat fast food at least once per week. She wants to
create a 95% Confidence interval which has an error bound of at most 2%. How many people should be polled to
create the confidence interval?
Answer: 2401
Minimum Sample Size p for Proportion
Confidence Level
0 Enter decimal Sample Proportion 0.5 If sample proportion unknown enter 0. Error 0.02 Write percentage as decimal z-Value
0 Minimum Sample Size 2401
17. Suppose a clothing store wants to determine the current percentage of customers who are over the age of
forty. How many customers should the company survey in order to be 92% confident that the estimated (sample)
proportion is within 5% of the true population proportion of customers who are over the age of 40?
Answer: 307
Minimum Sample Size p for Proportion
Confidence Level 0.920 Enter decimal Sample Proportion 0.5 If sample proportion unknown enter 0. Error 0.05 Write percentage as decimal z-Value 1. Minimum Sample Size 307
18. Suppose the scores of a standardized test are normally distributed. If the population standard
deviation is 2 points, what minimum sample size is needed to be 90% confident that the sample mean is within 1 point of the true population mean? Be sure to round up to the nearest integer.
Provide your answer below: 11
Minimum Sample Size μ for population mean
Confidence Level 0. StDev 2 Error 1 z-Value 1. Minimum Sample Size 11
19. The number of square feet per house are normally distributed with a population standard deviation
of 197 square feet and an unknown population mean. If a random sample of 25 houses is taken and results in a sample mean of 1820 square feet, find a 99 % confidence interval for the population mean. Round to 2
decimal places.
What is the correct interpretation of the 95 % confidence interval?
We can estimate that 98% of the time the test is taken, a student scores between 89.02 and 94.98 points.
We can estimate with 98% confidence that the true population mean score is
between 89.02 and 94.98 points.
We can estimate with 98% confidence that the sample mean score is between 89.02 and 94.98 points
22. The weights of running shoes are normally distributed with a population standard deviation of 3 ounces
and an unknown population mean. If a random sample of 23 running shoes is taken and results in a sample
mean of 18 ounces, find a 90 %confidence interval for the population mean. Round the final answer to
two decimal places.
Answer: 16.97 – 19.
23. The germination periods, in days, for grass seed are normally distributed with a population standard
deviation of 5 days and an unknown population mean. If a random sample of 17 types of grass seed is taken and results in a sample mean of 52 days, find a 80 % confidence interval for the population mean.
Select the correct answer below:
24. The speeds of vehicles traveling on a highway are normally distributed with a population standard
deviation of 7 miles per hour and an unknown population mean. If a random sample of 20 vehicles is taken and results in a sample mean of 60 miles per hour, find a 98 % confidence interval for the population mean.
Round the final answer to two decimal places.
Answer 56.36 – 63.
t or z Confidence Interval for μ
Confidence Level 0. n 20
Mean 60. StDev 7. pop stdev yes SE 1. z 2. Margin of Error 3. Lower Limit 56. Upper Limit 63.
25. Suppose finishing time for cyclists in a race are normally distributed and have a known population standard deviation of 6 minutes and an unknown population mean. A random sample of 18 cyclists is taken and gives a sample mean of 146 minutes. Find the confidence interval for the population mean with a 99 % confidence level. Answer: 142.36 – 149.
t or z Confidence Interval for μ
Confidence Level 0. n 18 Mean 146. StDev 6. pop stdev yes SE 1. z 2. Margin of Error 3. Lower Limit 142. Upper Limit 149.
26. Suppose the germination periods, in days, for grass seed are normally distributed. If the population standard deviation is 3 days, what minimum sample size is needed to be 90 % confident that the sample mean is within 1 day of the true population mean?
Answer: 25 seeds
Minimum Sample Size μ for population mean
Confidence Level 0. StDev 3 Error 1 z-Value 1. Minimum Sample Size 25
30. The yearly incomes, in thousands, for 24 random married couples living in a city are given below. Assume
the yearly incomes are approximately normally distributed. Use Excel to find the 95 % confidence interval for
- Level 0. Confidence - n
- Mean 23.
- StDev 1. - SE 0. pop stdev no - t 1. - Error 0. Margin of
- Lower Limit 22.
- Upper Limit 23.
- Lower margin of error = 22.69 and upper limit is 23.
- Lower Limit = 90.78 Upper Limit = 98. order. - Level 0. Confidence - n - Mean 94. - StDev 12. - SE 1. pop stdev yes - z 1. - 22. - 23. - 22. - 23. - 21. - 21. - 22. - 24. - 21. - 22. - 20. - 25. - 25. - 23. - 21. - 24. - Confidence Level 0. t or z Confidence Interval for μ - n - Mean 23. - StDev 1. - SE 0. pop stdev no - t 1. - Margin of Error 0. - Lower Limit 22. - Upper Limit 23.
- Answer: 58.984 – 59. the true mean, in thousands. Round your answers to three decimal places and use increasing order.
- 59.015 Mean 59. Data
- 58.962 Sample Standard Deviation 0.
59
t or z Confidence Interval for μ
Confidence Level 0. n 24 Mean 59. StDev 0. pop stdev no SE 0. t 2. Margin of Error 0. Lower Limit 58. Upper Limit 59.
31. A tax assessor wants to assess the mean property tax bill for all homeowners in a certain state. From a
survey ten years ago, a sample of 28 property tax bills is given below. Assume the property tax bills are approximately normally distributed. Use Excel to construct a 95 % confidence interval for the population mean
property tax bill. Round your answers to two decimal places and use increasing order.
Answer: 1185.91 – 1595.
32. The table below provides a random sample of 20 exam scores for a large geology class. Use Excel to construct a 90 % confidence interval for the mean exam score of the class. Round your answers to one
decimal place and use ascending order.
SE 2.
t 1.
Margin of Error 4. Lower Limit 153. Upper Limit 161.
34. Weights, in pounds, of ten-year-old girls are collected from a neighborhood. A sample of 26 is given below. Assuming normality, use Excel to find the 98 % confidence interval for the population mean weight μ. Round
your answers to three decimal places and use increasing order.
Answer: 66.497 – 77.
t or z Confidence Interval for μ
Confidence Level 0. n 26 Mean 71. StDev 11. pop stdev no SE 2. t 2. Margin of Error 5. Lower Limit 66. Upper Limit 77.
35. A sample of 22 test-tubes tested for number of times they can be heated on a Bunsen burner before they crack is given below. Assume the counts are normally distributed. Use Excel to construct a 99 % confidence interval for μ. Round your answers to two decimal places and use increasing order.
Answer: 1071.77 – 1477.
36. The monthly incomes from a random sample of 20 workers in a factory is given below in dollars. Assume the population has a normal distribution and has standard deviation $ 518. Compute a 98 % confidence
interval for the mean of the population. Round your answers to the nearest dollar and use ascending order.
Answer: 11,833 – 12,
37. Assume the distribution of commute times to a major city follows the normal probability distribution and
the standard deviation is 4.5 minutes. A random sample of 104 commute times is given below in minutes. Use Excel to find the 98 %confidence interval for the mean travel time in minutes. Round your answers to one
decimal place and use ascending order.
Answer: 25.9 – 27.
38. Installation of a certain hardware takes a random amount of time with a standard deviation of 7 minutes. A computer technician installs this hardware on 50 different computers. These times are given in the accompanying dataset. Compute a 95 % confidence interval for the mean installation time. Round your
answers to two decimal places and use ascending order.
Answer: 40.76 – 44.
39. Assume that farm sizes in a particular region are normally distributed with a population standard deviation
of 150 acres. A random sample of 50 farm sizes in this region is given below in acres. Estimate the mean farm size for this region with 90 %confidence. Round your answers to two decimal places and use ascending
order.
Answer: 474.87 – 544.
40. The amounts of time that customers stay in a certain restaurant for lunch is normally distributed with a
standard deviation of 17 minutes. A random sample of 50 lunch customers was taken at this restaurant. Construct a 99 % confidence interval for the true average amount of time customers spend in the restaurant
for lunch. Round your answers to two decimal places and use ascending order.
Answer: 44.89 – 57.
Confidence Level 0. n 50 Mean 42. StDev 7. pop stdev y SE 0. z 1. Margin of Error 1. Lower Limit 40. Upper Limit 44.
the 98 % confidence interval for the true mean age of players in this league. Round your answers to three
decimal places and use ascending order.
Answer: 27.579 – 29.
t or z Confidence Interval for μ
Confidence Level 0. n 41 Mean 28. StDev 2. pop stdev yes SE 0. z 2. Margin of Error 0. Lower Limit 27. Upper Limit 29.
44. In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample
of 25 pieces of carry-on luggage was collected and weighed in pounds. Assume that the population is normally distributed with a standard deviation of 5 pounds. Find the 95 % confidence interval of the mean
weight in pounds. Round your answers to two decimal places and use ascending order.
Answer: 15.36 – 19.
t or z Confidence Interval for μ
Confidence Level 0. n 25 Mean 17. StDev 5. pop stdev yes SE 1. z 1. Margin of Error 1. Lower Limit 15. Upper Limit 19.
45. A company wants to determine a confidence interval for the average CPU time of its teleprocessing
transactions. A sample of 70 random transactions in milliseconds is given below. Assume that the transaction times follow a normal distribution with a standard deviation of 600 milliseconds. Use Excel to determine a 98 % confidence interval for the average CPU time in milliseconds. Round your answers to the nearest
integer and use ascending order.
Answer: 5907 – 6240
t or z Confidence Interval for μ
Confidence Level 0. n 70 Mean 6,073. StDev 600. pop stdev yes SE 71. z 2. Margin of Error 166. Lower Limit 5906. Upper Limit 6240.
46. The number of hours worked per year per adult in a state is normally distributed with a standard deviation
of 37. A sample of 115 adults is selected at random, and the number of hours worked per year per adult is given below. Use Excel to calculate the 98 % confidence interval for the mean hours worked per year for
adults in this state. Round your answers to two decimal places and use ascending order.
Answer: 2090.03 – 2106.
47. An automobile shop manager timed 27 employees and recorded the time, in minutes, it took them to change a water pump. Assuming normality, use Excel to find the 99 % confidence interval for the true mean.
Round your answers to three decimal places and use increasing order.
Answer: 15.499 – 19.
t or z Confidence Interval for μ
Confidence Level 0. n 27 Mean 17. StDev 3. pop stdev no SE 0. t 2. Margin of Error 1. Lower Limit 15. Upper Limit 19.
48. A type of golf ball is tested by dropping it onto a hard surface from a height of 1 meter. The height it bounces is known to be normally: distributed. A sample of 25 balls is tested and the bounce heights are given below. Use Excel to find a 95 %confidence interval for the mean bounce height of the golf ball. Round your
answers to two decimal places and use increasing order.
Answer: 79.95 – 82.
t or z Confidence Interval for μ
Answer: 385
Minimum Sample Size p for
Proportion
Confidence Level 0. Sample Proportion 0. Error 0. z-Value 1. Minimum Sample Size 385
52. Suppose an automotive repair company wants to determine the current percentage of customers who keep
up with regular vehicle maintenance. How many customers should the company survey in order to
be 95 % confident that the estimated (sample) proportion is within 4 percentage points of the true population
proportion of customers who keep up with regular vehicle maintenance?
Answer: 601
Minimum Sample Size p for
Proportion
Confidence Level
0 Sample Proportion 0. Error 0. z-Value
0 Minimum Sample Size 601
53. Suppose a clothing store wants to determine the current percentage of customers who are over the age of
forty. How many customers should the company survey in order to be 92 % confident that the estimated (sample) proportion is within 5 percentage points of the true population proportion of customers who are over
the age of forty?
Answer: 307
Minimum Sample Size p for
Proportion
Confidence Level
0 Sample Proportion 0. Error 0. z-Value
1 Minimum Sample Size 307
54. The average height of a population is unknown. A random sample from the population yields a
sample mean of x¯=66.3inches. Assume the sampling distribution of the mean has a standard deviation of σx¯=0.8 inches. Use the Empirical Rule to construct a 95% confidence interval for the true population mean height.
Provide your answer below: 64.7 – 67.
55. In a random sample of 30 young bears, the average weight at the age of breeding is 312 pounds. Assuming the population ages are normally distributed with a population standard deviation is 30 pounds, use the Empirical Rule to construct a 68 %confidence interval for the population average of young bears at the
age of breeding. Do not round intermediate calculations. Round only the final answer to the nearest pound.
Remember to enter the smaller value first, then the larger number.
Answer: 307 – 317
56. In a food questionnaire, a random sample of teenagers were asked whether they like pineapple
pizza. The questionnaire resulted in a sample proportion of p′=0.43, with a sampling standard deviation of σp′=0.06, who like this type of pizza. Write a 99.7% confidence interval using the Empirical Rule for the true proportion of teenagers who like
pineapple pizza.
Answer: 0.25 - 0.
57. A marine biologist is interested in whether the Chinook salmon, a particular species of salmon in
the Pacific Northwest, are getting smaller within the last decade. In a random sample of this species
of salmon, she found the mean length was x¯=36inches with a margin of error of 9 inches.
Construct a confidence interval for the mean length of Chinook salmon.
Answer: 27 - 45
58. A researcher is trying to estimate the population mean for a certain set of data. The sample mean is 45 , and the error bound for the mean is 9 , at a 99.7% confidence level. (So, x¯= 45 and EBM = 9 .) Find and
interpret the confidence interval estimate.
Answer: We can estimate, with 99.7% confidence that the true value of the population mean is between 36 and 54.
59. A random sample of registered voters were asked about an issue on the ballot of an upcoming
election. The proportion of those surveyed who plan to vote "Yes" on the issue is 0.54, with a margin of error of 0.06.
Construct a confidence interval for the proportion of registered voters that plan to vote "Yes" on the issue.
Answer: .48 -.
