Download Find the point estimate for the following

Statistics
Chapter 7 Review
Name: _____________________
Find the point estimate for the following.
1. Find the point estimate of population mean of the following data.
1.0
1.93
0.83
0.91
1.08
1.09
1.10
1.88
Point Estimate: ____________
1.36
2. Find the point estimate of population proportion: A New York Times poll on women’s issues interviewed 1025
women randomly selected from the United States, excluding Alaska and Hawaii. The poll found 42% of the women said
that do not get enough time for themselves.
Point Estimate: _____________
Determine which critical value should be used in the following situations - z/2, t/2, or neither.
3. n = 15, s = 2.36, the population has a normal distribution
__________________________
4. n = 15, =2.36, the population is skewed
__________________________
5. n = 15, =2.36, the population is normally distributed
__________________________
6. n = 51, s = 2.36, the population is skewed
__________________________
Find the critical value you would use to estimate population mean.
7. n = 15, s = 2.36, the population has a normal distribution, 98% degree of confidence __________________________
8. n = 51, s = 2.36, the population has a normal distribution, 99% degree of confidence __________________________
Find Margin of Error for population mean. Assume the population is normally distributed.
9. n = 20, =1.9; Degree of Confidence is 86%
__________________________
10. n = 35, s = 35.2; Degree of Confidence is 99%
__________________________
11. n = 20, s = 12.75; Degree of Confidence is 80%
__________________________
Answer the following:
12. A gas station sold a total of 8019 gallons of gas on 45 randomly picked days. Suppose the amount sold on a day is
normally distributed with a standard =90 gallons. Construct confidence intervals for the true man amount  sold on a
day with the following confidence levels.
a. 98% degree of confidence
Critical Value: _______
Margin of Error: ____ __
Confidence Interval: _________
b. 80% degree of confidence
Critical Value: _______ Margin of Error: ______ Confidence Interval: ___________
13. From past records, the seasonal rainfall in a county when observed over sixteen randomly picked years yielded a
mean rainfall of 20.8 inches. If it can be assumed from past experience that rainfall during a season is normally
distributed with =2.8 inches, construct confidence intervals for the true mean rainfall  with the following confidence
intervals.
a. 90%
Critical Value: _______
Margin of Error: _____ ________
Confidence Interval: _______________
b. 95%
Critical Value: _______
Margin of Error: _____ ________
Confidence Interval: _______________
14.
When sixteen cigarettes of a particular brand were tested in a laboratory for the amount of tar content, it was
found that their mean content was 18.3 milligrams with s = 1.8 milligrams. Construct the 90% confidence interval for
the mean tar content  in the population of cigarettes in this brand.
Critical Value: _______
Margin of Error: _____ ________
Confidence Interval: _______________
15.
The data given below represent the time (in minutes) taken by 14 randomly selected students to complete a
national exam.
99
109
69
64
100
65
100
104
92
83
87
73
79
65
Based on these data, determine the true mean estimated time and the margin of error at the 95% degree of confidence
level.
Sample Mean: _____________Sample Standard Deviation: _________ Margin of Error: __________________
Confidence Interval: _____________________
Find p̂ and q̂ for the given information.
16. n=60, x=18
______
_______
17. n = 100, x = 62
___________
__________
Find the margin of error for the population proportion p.
17. n = 78, x = 30, Degree of Confidence is 90%
__________________
18. n = 80, x = 52, Degree of Confidence is 88 %
__________________
Construct the confidence interval for the corresponding population proportion p at the indicated level of confidence if
the following information is given.
19. In a study with a new vaccine involving fifty-three lung cancer patients, thirty-three survived five years after surgery.
Obtain the 98% confidence interval for the true proportion of patients surviving five years after surgery with the new
vaccine.
Critical Value: ____________ P-hat: _______ q-hat: __________ Margin of Error: ________________
Confidence Interval: ___________________
Interpret the interval:
20. In order to test the effectiveness of a flu vaccine, it was administered to 650 people who were selected at random.
At the end of the flu season it was determined that 553 of individuals did not get the flu. Using a 90% confidence
interval, estimate the true proportion of people who would not get the flu if given the vaccine.
Critical Value: _____________ P-hat: _______ q-hat: _______ Margin of Error: ____________
Confidence Interval: _______________
Interpret the interval:
Finding sample size to estimate population proportion.
21. A new vaccine is to be tested on the market. Find how large a sample should be drawn if we want to be 95%
confident that the estimate will not be in error of the true proportion of success by more than:
a.) 0.1
n = ________________
b.) 0.02
n = ________________
22.
A coffee company wants to estimate the true proportion in the U.S. population that drinks its brand. How many
individuals should be surveyed to be 99% confident of having the true proportion of people drinking the brand
estimated to with 0.018? Based on pilot study, the percentage of people drinking this particular brand of coffee was
48.1%.
n = __________________
Find sample size used to estimate population mean.
23.
A population has a normal distribution with 225. Find how large a sample must be drawn in order to be 95%
confident that the sample mean will not differ from the population mean by more than 2 units.
n = _____________
24. Suppose the breaking strength of cables (in pounds) is known to have a normal distribution with a standard
deviation = 6 pounds. Find how large a sample must be taken so as to be 90% confident that the sample mean
breaking strength will not differ from the true mean breaking strength by more than 0.75 pounds.
n = _____________
Find the point estimate and margin of error.
25. Find the point estimate and margin of error of population mean for the given confidence interval.
56.54 < < 59.86
Point Estimate: _________________
Margin of Error: __________________
26. Find the point estimate and margin of error of population variance for the given confidence interval.
0.34 < p < 0.46
Point estimate: _________________
Margin of Error: _________________