1. Find the minimum sample size n needed to estimate µ for the given values of c, s, and E.
C= 0.98, s= 9.3, and E= 1
N= ______ (round to the nearest whole number)
2. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.
A random sample of 40 home theater systems has a mean price of $142.00 and a standard deviation is $15.30
Construct a 90% confidence interval for the population mean.
The 90% confidence interval is (______,______) (Round to two decimal places as needed)
3. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.
A random sample of 38 gas grills has a mean price of $638.80 and a standard deviation of $55.30
Construct a 90% confidence interval for the population mean.
The 90% confidence interval is (______,______) (Round to One decimal place as needed)
4. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.
A random sample of 50 eight-ounce servings of different juice drinks has a mean of 84.4 calories and a standard deviation of 41.8 calories.
The 90% confidence interval is (______,______) (Round to One decimal place as needed)
5. People were polled on how many books they read the previous year. How many subjects are needed to estimate the number of books read the previous year within one book with 90% confidence? Initial survey results indicate that o= 16.7 books.
A 90% confidence level requires ______ subjects. (Round up to the nearest whole number as needed)
6. A doctor wants to estimate the HDL cholesterol of all 20 to 29 year old females. How many subjects are needed to estimate the HDL cholesterol within 3 points with 99% confidence assuming o= 18.8? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?
A 99% confidence level requires ______ subjects. (Round up to the nearest whole number as needed)
7. Construct the indicated confidence interval for the population mean µ using (a) a t-distribution.
(a) The 90% confidence interval using a t-distribution is (______,______) (Round to one decimal place as needed)
(b) If you had incorrectly used a normal distribution, which interval would be wider?
8. In the following situation, assume the random variable is normally distributed and use a normal distribution or a t-distribution to construct a 90% confidence interval for the population mean. If convenient, use technology to construct the confidence interval.
(a) In a random sample of 10 adults from a nearby county, the mean waste generated per person per day was 4.29 pounds and the standard deviation was 1.08 pounds.
For the sample of 10 adults, the 90% confidence interval is (______,______) (Round to two decimal places as needed)
(b) Repeat part (a), assuming the same statistics came from sample size 400. Compare the results. ___________________________
9. In a survey of 648 males ages 18-64, 394 say they have gone to the dentist in the past year.
Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If convenient, use the technology to construct the confidence intervals.
The 90% confidence interval for the population proportion is (______,______) (Round to three decimal places as needed)
10. In a survey of 8000 women, 5431 say they change their nail polish once a week. Construct a 90% confidence interval for the population proportion of women who change their nail polish once a week.
A 90% confidence interval for the population proportion is (_______,_______) (Round to three decimal places as needed)