WorksheetsSample Size of Confidence Intervals
Total questions: 20
Worksheet time: 20mins
A population has a standard deviation of σ = 17.3. How large of a sample must be drawn so that a 95% confidence interval for µ will have a Margin of Error equal to 1.4?
586.6
587
586
585
The lifetime of a certain type of batter is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.
What is the Confidence Interval to one decimal place?
(114.5, 125.6)
(112.8, 127.4)
(112.82, 127.38)
(114.56, 125.64)
A person selects a random sample of 15 credit cards and determines the annual interest rate, in percent, of each one. The sample mean is 12.42 with a sample standard deviation of 1.3. It is desired to construct a 90% Confidence Interval.
Find the Standard Error to three decimal places.
0.336
0.33566
13.156
0.087
A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content μ?
90% confidence; n = 25
90% confidence; n = 50
95% confidence; n = 25
95% confidence; n = 50
n=100 at any confidence level
A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?
60
75
90
180
Which of the following would result in a smaller minimum sample size?
Increasing the confidence level
Not having a preliminary estimate for p-hat
Decreasing the confidence level
Decreasing the margin of error
A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?
60
75
90
180
In a recent poll of 803 randomly selected baseball fans in Connecticut, 44% said their favorite team was the Yankees. If researchers wanted to reduce the margin of error to at most 2%, how many baseball fans do they have to randomly select? Use 95% confidence
1564
2367
803
3170
To achieve a narrower confidence interval for a given confidence level, one should:
Increase the sample size.
Decrease the sample size.
Increase the standard deviation.
Decrease the confidence level.
What happens to the margin of error if the sample size is quadrupled, all else being equal?
It is halved.
It is doubled.
It remains the same.
It is quadrupled.
A research company wants to estimate the proportion of people who like oatmeal. They want the confidence level to be 95%. The company gets 325 people to sign up for the survey, but on the day that the survey is issued, only 250 people show up and take the survey. What happens to the confidence interval?
It stays the same
It gets narrower
It gets wider
Not enough information
Increasing the sample size __________ the confidence interval.
increases
decreases
does not affect
there is not enough evidence to determine the answer
To decrease the margin of error in a confidence interval, you should:
Increase the confidence level
Decrease the sample size
Increase the sample size
Decrease the confidence level
A preliminary study suggests that 17% of people agree on an issue. How large must your sample size be so you could be within ± 5% with 95% confidence?
217
30
385
152
In a recent poll of 803 randomly selected baseball fans in Connecticut, 44% said their favorite team was the Yankees. If researchers wanted to reduce the margin of error to at most 2%, how many baseball fans do they have to randomly select fir a 95% confidence interval?(Note: p-hat is estimated to be .44)
1564
2367
803
3170
You are given two sets of data measuring the same information, both with the same sample size. Set A has a larger Standard Error than Set B. If you were looking for a 99.8% Confidence Interval, which set would have a larger Margin of Error?
Set A
Set B
Not enough information
I have no idea what you're asking me to do
A large sample has mean of 7.1 and Standard Error of 2.3.
Construct a 90% Confidence Interval for the population mean µ (to two decimal places).
(3.32, 10.88)
(3.8, 7.1)
(3.3, 10.9)
(3.3165, 10.8835)
An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean score was 105.2. Scores on this test are known to have a standard deviation of 10. It is desired to construct a 90% confidence interval for the mean IQ scores of the students at the college.
Find the Margin of Error to two decimal places.
1.90
1.89
1.899
1.99
Which of the following changes to a study would result in a narrower confidence interval?
increasing the confidence level, increasing the sample size
decreasing the confidence level, decreasing the sample size
increasing the confidence level, decreasing the sample size
decreasing the confidence level, increasing the sample size.
A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse?
0.148 < p < 0.192
0.136 < p < 0.204
0.144 < p < 0.196
0.139 < p < 0.201
