1. When constructing a confidence interval for a population mean from a sample w
ID: 3261033 • Letter: 1
Question
1. When constructing a confidence interval for a population mean from a sample with size 17, the number of degrees of freedom for the critical value is ________
2. Which of the following are true statements:
When the number of degrees of freedom is small, the student’s t distribution is close to the normal distribution.
XX The student’s t curve is more spread out than the normal curve.
The student’s t distribution can be used to find a confidence interval for the population mean if outliers are present in a small sample.
XX The assumptions for constructing a confidence interval for the population mean when the population standard deviation is unknown are: 1)We have a simple random sample 2)Either the sample size is large (>30) or the population is approximately normal.
3. Match the TI-84 Plus calculator command that would be used to find the confidence interval in each case. If the confidence interval cannot be constructed, choose “Cannot be done”
Sample size=4
Sample mean-0.86
Population Standard Deviation=0.0021 1. TInterval
Sample size=100 2. Cannot be done
Sample mean=20
Sample Standard Deviation=4 3. ZInterval
Sample size=85
Sample mean=1091
Sample Standard Deviation=0.18
Population is not normal
Sample Size =12
Sample mean= 94
Population Standard Deviation-14
Population is normal
Sample size=21
Sample mean=14.2
Population Standard Deviation=0.18
Population is not normal
3
Sample size=19
Sample mean=0.26
Population Standard Deviation=0.08
Population is not normal
4. A company has developed a new type of light bulb, and wants to estimate its mean lifetime. A simple random sample of 12 bulbs had a sample mean lifetime of 833 hours with a sample standard deviation of 28 hours. It is reasonable to believe that the population is approximately normal. Find the lower bound of the 95% confidence interval for the population mean lifetime of all bulbs manufactured by this new process. Round to the nearest integer.
5. A random sample of 40 videos posted to YouTube was selected. A month later, the number of times that each had been viewed was tabulated. The mean number of viewings was 144 with a sample standard deviation of 275. Find the upper bound of the 99% confidence interval for the mean number of times videos posted to YouTube have been viewed in the first month. Round to the nearest integer.
6. A random sample of 13 DVD movies had a mean length of 115.2 minutes, with a standard deviation of 66.2 minutes. Find the lower bound of the 90% confidence interval for the true mean length of all Hollywood movies. Assume movie lengths to be approximately normally distributed. Round to one decimal place.
7. Six measurements were made of the mineral content (in percent) of spinach, with the following results. It is reasonable to assume that the population is approximately normal.
19.1, 20.1, 20.8, 21.1, 20.5,19.1 Find the lower bound of 95% confidence interval for the true mineral content. Round to three decimal places.
8. Following are interest rates (annual percentage rates) for a 30-year-fixed-rate mortgage from a sample of lenders in a certain city. It is reasonable to assume that the population is approximately normal.
4.327, 4.461, 4.547, 4.341, 4.365, 4.365, 4.842 Find the upper bound of the 99% confidence interval for the mean rate. Round to three decimal places.
Explanation / Answer
1) When constructing a confidence interval for a population mean from a sample with size 17, the number of degrees of freedom for the critical value is _
degrees of freedom df= n-1 = 17-1=16
2) these statements are true
..When the number of degrees of freedom is small, the student’s t distribution is close to the normal distribution.
.. The student’s t curve is more spread out than the normal curve.
..The student’s t distribution can be used to find a confidence interval for the population mean if outliers are present in a small sample.
3)
Sample size=4
Sample mean-0.86
Population Standard Deviation=0.0021 cannot be done
Sample size=100 . Cannot be done
Sample mean=20
Sample Standard Deviation=4
Sample size=85
Sample mean=1091
Sample Standard Deviation=0.18 cannot be done
Population is not normal
Sample Size =12
Sample mean= 94
Population Standard Deviation-14 TI caluclator
Population is normal
Sample size=21
Sample mean=14.2
Population Standard Deviation=0.18 cannot be done
Population is not normal
3
Sample size=19
Sample mean=0.26
Population Standard Deviation=0.08 cannot be done
Population is not normal
4) 833-+ 1.96* 28 /sqrt(12)
833 -+ 15.84
(848.84, 817.16)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.