225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
Week 6 Questions on Confidence Intervals
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.
(0.42 - 0.07), (0.42 + 0.07) = (0.35), (0.49)
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. (31-3), 31+3) = (28), (34)
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.
(0.83 – 0.11), (0.83 + 0.11) = (0.72), (0.94)
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.
(.25 - .05). (.25 + .05) = (0.20), (.30)
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 + 0.82
225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
, 225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
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
Mean 25.8 23.1043
22.2
Sample Standard Deviation 1.3693
22.5
22.8
24.6
24
22.6
23.6
22.8
23.1
21.5
21.4
22.5
24.5
21.5
22.5
20.5
23
25.1
25.2
23.8
21.8
24.1
Confidence
Level 0.900
n 32
Mean 23.1043
1.3693
StDev
no
pop stdev
SE 0.242060
t Margin of 1.696
Error
0.410534
Lower Limit
22.693766
Upper Limit 23.514834
225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
, 225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
Lower margin of error = 22.69 and upper limit is 23.51
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 order.
Lower Limit = 90.78 Upper Limit = 98.22
Confidence
Level 0.950
n 40
Mean 94.5000
12.0000
StDev
yes
pop stdev
SE 1.897367
z Margin
1.960
Error Lower Limit
Upper Limit 3.718839
90.781161
98.218839
9. In the survey of 603 adults, 98 said that they regularly lie to people conducting surveys. Create a 99%
confidence interval for the proportion of adults who regularly lie to people conducting surveys. Use excel
to create the confidence interval rounding to 4 decimal places.
Lower Limit = 0.1238 Upper Limit = 0.2012
Confidence Level 0.990
n Number of Successes 603
98
Sample Proportion 0.162521
SE 0.015024
z 2.576
0.038702
Margin of
0.123819
Error Lower 0.201222
Limit Upper
Limit
225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
And Answers Correctly Verified RATED A+
Week 6 Questions on Confidence Intervals
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.
(0.42 - 0.07), (0.42 + 0.07) = (0.35), (0.49)
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. (31-3), 31+3) = (28), (34)
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.
(0.83 – 0.11), (0.83 + 0.11) = (0.72), (0.94)
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.
(.25 - .05). (.25 + .05) = (0.20), (.30)
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 + 0.82
225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
, 225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
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
Mean 25.8 23.1043
22.2
Sample Standard Deviation 1.3693
22.5
22.8
24.6
24
22.6
23.6
22.8
23.1
21.5
21.4
22.5
24.5
21.5
22.5
20.5
23
25.1
25.2
23.8
21.8
24.1
Confidence
Level 0.900
n 32
Mean 23.1043
1.3693
StDev
no
pop stdev
SE 0.242060
t Margin of 1.696
Error
0.410534
Lower Limit
22.693766
Upper Limit 23.514834
225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
, 225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
Lower margin of error = 22.69 and upper limit is 23.51
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 order.
Lower Limit = 90.78 Upper Limit = 98.22
Confidence
Level 0.950
n 40
Mean 94.5000
12.0000
StDev
yes
pop stdev
SE 1.897367
z Margin
1.960
Error Lower Limit
Upper Limit 3.718839
90.781161
98.218839
9. In the survey of 603 adults, 98 said that they regularly lie to people conducting surveys. Create a 99%
confidence interval for the proportion of adults who regularly lie to people conducting surveys. Use excel
to create the confidence interval rounding to 4 decimal places.
Lower Limit = 0.1238 Upper Limit = 0.2012
Confidence Level 0.990
n Number of Successes 603
98
Sample Proportion 0.162521
SE 0.015024
z 2.576
0.038702
Margin of
0.123819
Error Lower 0.201222
Limit Upper
Limit
225N Week 6 Confidence Intervals MATH EXAM best Questions
And Answers Correctly Verified RATED A+
