Stats - Ch. 7
Find the margin of error for the given confidence level and values of x and n. x = 111, n = 194, confidence level 99%
0.093
A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 6 percentage points with 90% confidence?
130
What is the value for x2 right for a 98% confidence interval when n=12?
24.725
An economics professor randomly selected millionaires in the United States. The average age of these millionaires was 54.8 years. If the standard deviation of the entire population of millionaires is 7.9 years, find the 95% confidence interval for the mean age of all United States millionaires.
53.3 μ
Scores on the math SAT are normally distributed. A sample of 15 SAT scores had a standard deviation s=80. Construct a 95% confidence interval for the population standard deviation σ.
58.57 σ 126.17
A random sample of 9 TI-89 Titanium calculators being sold over the internet had the following prices, in dollars. 142, 149, 147, 146, 145, 148, 154, 136, 131 Assume the population standard deviation is σ =30 and that the population is approximately normal. Construct a 95% confidence interval for the mean price for all the TI-89's being sold over the internet.
(124.6, 163.8)
A random sample of 9 TI-89 Titanium calculators being sold over the internet had the following prices, in dollars. 142, 149, 147, 146, 145, 148, 154, 136, 131 Assume the population standard deviation is σ and that the population is approximately normal. Construct a 95% confidence interval for the mean price for all the TI-89's being sold over the internet.
(124.6, 163.8)
A chi-square distribution is negatively skewed.
False
Find the margin of error for the given confidence level and values of x and n. x = 114, n = 216, confidence level 95%
0.067
A random sample of 95 printers discovered that 25 of them were being used in small businesses . Find the 99% limit for the population proportion of printers that are used in small businesses.
0.146 p 0.380
A random sample of 70 printers discovered that 20 of them were being used in small businesses . Find the 99% limit for the population proportion of printers that are used in small businesses.
0.147 p 0.425
If p-hat is equal to 0.77, then q-hat is equal to ______.
0.23
A random sample of 95 printers discovered that 30 of them were being used in small businesses . Find the 90% limit for the population proportion of printers that are used in small businesses.
0.237 p 0.395
A random sample of 80 printers discovered that 30 of them were being used in small businesses . Find the 95% limit for the population proportion of printers that are used in small businesses.
0.269 p 0.481
In a survey of 246 registered voters, 132 of them wished to see Mayor Waffleskate lose her next election. Find a point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated.
0.537
In a survey of 312 registered voters, 169 of them wished to see Mayor Waffleskate lose her next election. Find a point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated.
0.542
A food snack manufacturer samples 13 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.2 oz and the sample standard deviation is 0.70 oz., find the 95% confidence interval of the true mean.
14.8 μ 15.6
Boxes of raisins are labeled as containing 22 ounces. Following are the weights, in ounces, of a sample of 12 boxes. It is reasonable to assume that the population is approximately normal. 21.72, 21.75, 21.62, 21.92, 22.10, 22.13, 22.25, 22.26, 22.04, 21.88, 22.02, 22.15 Construct a 95% confidence interval for the mean weight.
21.853 μ 22.120
A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 1000 pounds. At a 90% level, how many elephants need to be weighed so the average weight will be accurate to within 300 pounds?
31
5 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight.
7.9 μ 10.7
A simple random sample of kitchen toasters is to be taken to determine the mean operational lifetime in hours. Assume that the lifetimes are normally distributed with population standard deviation σ =30 hours. Find the sample size needed so that a 98% confidence interval for the mean lifetime will have a margin of error of 8.
77
A retailer wants to estimate with 99% confidence the number of people who shop at his store. A previous study showed that 24% of those interviewed had shopped at his store. He wishes to be accurate within 3% of the true proportion. The minimum sample size necessary would be 1,100.
False
When computing a confidence interval for a population mean using raw data, round off to two more decimal places than the number of decimal places in the original data.
False
Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal. 162, 151, 158, 170, 173, 161 Based on a 99% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 185.5? (Hint: you should first calculate the 99% confidence interval for the mean magnesium ion concentration.)
No.
The t-distribution has a variance that is greater than one.
True
In a study of 100 new cars, 28 are white. Find p-hat and q-hat, where p-hat is the proportion of new cars that are white.
p-hat= 0.28, q-hat= 0.72
Find the standard error for the given values of x and n. x = 125, n = 259
0.031
An interval estimate may or may not contain the true value of the parameter being estimated.
True
The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter.
True
A random sample of 75 printers discovered that 35 of them were being used in small businesses . Find the 99% limit for the population proportion of printers that are used in small businesses.
0.318 p 0.616
Use the given data to construct a confidence interval of the requested level. x = 98, n = 223, confidence level 99%
0.354 p 0.525
The prices (in dollars) for a graphing calculator are shown below for 8 online vendors. Estimate the true mean price for this particular calculator with 95% confidence. 156, 149, 124, 127, 135, 133, 132, 123
125.0 μ 144.8
If a population has a standard deviation of 14, what is the minimum number of samples that need to be averaged in order to be 95% confident that the average of the means is within 2 of the true mean?
189
Find the critical value tα/2 needed to construct a confidence interval of the given level with given sample size. Level 95%, sample size 11
2.228
In a study using 8 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is
a t distribution with 7 degrees of freedom.
Find the point estimate for the given values of x and n. x = 122, n = 201
0.607
What is the 90% confidence interval for the variance of exam scores for 28 algebra students, if the standard deviation of their last exam was 12.7 ?
108.6 σ2
The prices (in dollars) for a graphing calculator are shown below for 8 online vendors. Estimate the true mean price for this particular calculator with 95% confidence. 121, 125, 151, 129, 127, 133, 121, 125
120.9 μ 137.1
Construct a 95% confidence interval for the population standard deviation σ if a sample of size 18 has standard deviation s=20.
15.01 σ 29.98
A sample of 132 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10, with 10 corresponding to "completely effective" and 1 corresponding to "completely ineffective". The average rating was 5.7 and the standard deviation was 4.7. Construct a 95% confidence interval for the mean score.
4.9 μ 6.5
It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets?
0.620 p
A sample of size n=56 is drawn from a population whose standard deviation is σ= 4.5. Find the margin of error for a 95% confidence interval for μ.
1.18
Find the critical value zα/2 needed to construct a(n) 79% confidence interval.
1.35
Find the critical value zα/2 needed to construct a(n) 83% confidence interval.
1.37
Measurements were made of the milk fat content (in percent) in six brands of feta cheese (a variety of goat cheese), with the following results. Assume that the population is normally distributed. 16.7, 20.1, 19.6, 21.7, 22.0, 23.9 Construct a 90% confidence interval for the population standard deviation σ.
1.66 σ 5.16
Following are the heights in inches of 12 two-year-old apple trees. Assume that the population is normally distributed. 37.4, 34.8, 37.8, 38.6, 36.4, 33.1, 34.8, 33.8, 38.0, 31.5, 38.0, 38.3 Construct a 95% confidence interval for the population standard deviation σ.
1.68 σ 4.02
Following are the heights in inches of 12 two-year-old apple trees. Assume that the population is normally distributed. 36.2, 37.7, 34.7, 37.3, 42.3, 37.0, 41.5, 38.6, 39.5, 39.2, 42.2, 34.7 Construct a 90% confidence interval for the population standard deviation σ.
1.98 σ 4.10
A sample of 145 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10, with 10 corresponding to "completely effective" and 1 corresponding to "completely ineffective". The average rating was 3.4 and the standard deviation was 4.9. Construct a 95% confidence interval for the mean score.
2.6 μ 4.2
Find the critical value zα/2 needed to construct a(n) 99.1% confidence interval.
2.61
A college believes that 26% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points with 95% confidence?
296
Measurements were made of the milk fat content (in percent) in six brands of feta cheese (a variety of goat cheese), with the following results. Assume that the population is normally distributed. 17.4, 26.2, 23.8, 8.1, 25.3, 17.5 Construct a 99% confidence interval for the population standard deviation σ.
3.75 σ 23.90
A report states that 38% of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 6 percentage points with 98% confidence?
356
Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 11 pipes has a standard deviation of 8.6 inches.
6.0 σ 15.1
7 squirrels were found to have an average weight of 8.7 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight.
7.7 μ 9.7
A study of 75 bolts of carpet showed that their average length was 72.2 yards. The standard deviation of the population is 2.6 yards. Which of the following is the 98% confidence interval for the mean length per bolt of carpet?
71.5 μ 72.9
Construct a 99% confidence interval for the population standard deviation σ if a sample of size 11 has standard deviation s=15.
9.45 σ 32.31
The t-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.
False
The value for x2 left for a 95% confidence interval when n=15 is 26.119.
True
In a study of 100 new cars, 29 are white. Find p-hat and q-hat, where p-hat is the proportion of new cars that are white.
p-hat= 0.29, q-hat= 0.71
Find the critical value zα/2 needed to construct a(n) 98.9% confidence interval.
2.54
A random sample of magnesium concentrations (in parts per million, or ppm) in ground water from various locations follows. Estimate the mean concentration of magnesium in ppm with 90% confidence. Assume σ = 13. 39, 10, 73, 50, 92, 42, 33, 125, 118, 35, 28, 123, 124, 69, 30, 114, 14, 121, 11, 85, 51, 13, 37, 105, 118, 33, 25, 19, 33, 6, 7, 15, 12, 106, 14
51.5 μ 58.8
A random sample of magnesium concentrations (in parts per million, or ppm) in ground water from various locations follows. Estimate the mean concentration of magnesium in ppm with 90% confidence. Assume σ =20. 44, 122, 34, 114, 5, 101, 68, 106, 100, 56, 42, 66, 36, 20, 18, 98, 101, 28, 89, 100, 125, 7, 31, 94, 21, 70, 38, 18, 60, 18, 98, 51, 30, 120, 68
57.2 μ 68.3
A random sample of 75 printers discovered that 25 of them were being used in small businesses . Find the 99% limit for the population proportion of printers that are used in small businesses.
0.193 p 0.473
A random sample of 70 printers discovered that 30 of them were being used in small businesses . Find the 90% limit for the population proportion of printers that are used in small businesses.
0.331 p 0.527
A random sample of 80 printers discovered that 35 of them were being used in small businesses . Find the 90% limit for the population proportion of printers that are used in small businesses.
0.346 p 0.530
A random sample of 65 printers discovered that 30 of them were being used in small businesses . Find the 90% limit for the population proportion of printers that are used in small businesses.
0.360 p 0.564
Find the critical value tα/2 needed to construct a confidence interval of the given level with given sample size. Level 90%, sample size 10
1.833
Following are the heights in inches of 12 two-year-old apple trees. Assume that the population is normally distributed. 31.9, 36.9, 40.7, 36.3, 39.4, 34.5, 36.9, 37.2, 40.3, 42.0, 41.0, 39.3 Construct a 99% confidence interval for the population standard deviation σ.
1.90 σ 6.09
Find the critical value zα/2 needed to construct a(n) 95% confidence interval.
1.96
A sample of size n=14 has a sample mean x = 11.9 and sample standard deviation s =2. Construct a 99% confidence interval for the population mean μ.
10.2 μ 13.6
A sample of size n=14 has a sample mean x=11.9 and sample standard deviation s=2.1. Construct a 99% confidence interval for the population mean μ.
10.2 μ 13.6
A recent poll of 700 people who work indoors found that 278 smoke. If the researchers want to be 98% confident of their results to within 3.5 percentage points, how large a sample is necessary?
1062
A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 2000 pounds. At a 90% level, how many elephants need to be weighed so the average weight will be accurate to within 300 pounds?
121
Find the values for x² left and x² right when α = .05 and n = 27.
13.844 and 41.923
The prices (in dollars) for a graphing calculator are shown below for 8 online vendors. Estimate the true mean price for this particular calculator with 95% confidence. 146, 136, 141, 143, 130, 122, 135, 155
130.0 μ 147.0
A sample of size n=11 has a sample mean x=15.6 and sample standard deviation s=2.4. Construct a 95% confidence interval for the population mean μ.
14.0 μ 17.2
A food snack manufacturer samples 13 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.2 oz and the sample standard deviation is 0.70 oz, find the 95% confidence interval of the true mean.
14.8 μ 15.6
A food snack manufacturer samples 11 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.2 oz and the sample standard deviation is 0.50 oz, find the 95% confidence interval of the true mean.
14.9 μ 15.5
A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.7 oz and the sample standard deviation is 0.50 oz., find the 95% confidence interval of the true mean.
15.2 μ 16.2
Find tα/2 when n =12 for the 95% confidence interval for the mean.
2.20
Find tα/2 when n=12 for the 95% confidence interval for the mean.
2.20
A sample of size n = 22 is drawn from a normal population. Find the critical value tα/2 needed to construct a 98% confidence interval.
2.518
Find the critical value zα/2 needed to construct a(n) 99.6% confidence interval.
2.88
In a sample of 55 mice, a biologist found that 44% were able to run a maze in 30 seconds or less. Find the 99% limit for the population proportion of mice who can run a maze in 30 seconds or less.
26.7% p 61.3%
Find tα/2 when n=12 for the 99% confidence interval for the mean.
3.11
A sample of 125 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10, with 10 corresponding to "completely effective" and 1 corresponding to "completely ineffective". The average rating was 4.1 and the standard deviation was 4.0. Construct a 95% confidence interval for the mean score.
3.4 μ 4.8
A previous analysis of paper boxes showed that the the standard deviation of their lengths is 11 millimeters. A packer wishes to find the 95% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within 4 millimeters?
30
A study of nickels showed that the the standard deviation of the weight of nickels is 150 milligrams. A coin counter manufacturer wishes to find the 98% confidence interval for the average weight of a nickel. How many nickels does he need to weigh to obtain an average accurate to within 20 milligrams?
306
A random sample of 50 voters found that 46% were going to vote for a certain candidate. Find the 95% limit for the population proportion of voters who will vote for that candidate.
32.2% p 59.8%
A researcher wants to construct a 99% confidence interval for the proportion of elementary school students in Seward County who receive free or reduced-price school lunches. What sample size is needed so that the confidence interval will have a margin of error of 0.07?
339
A study of nickels showed that the the standard deviation of the weight of nickels is 300 milligrams. A coin counter manufacturer wishes to find the 95% confidence interval for the average weight of a nickel. How many nickels does he need to weigh to obtain an average accurate to within 10 milligrams?
3458
A researcher wants to construct a 98% confidence interval for the proportion of elementary school students in Seward County who receive free or reduced-price school lunches. A state-wide survey indicates that the proportion is 0.60. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.06?
361
A sample of size n=11 is drawn from an approximately normal population whose standard deviation is σ=9.5. The sample mean is x=44.9 Construct a 90% confidence interval for μ.
40.19 μ 49.61
The winning team's score in 13 high school basketball games was recorded. If the sample mean is 54.3 points and the sample standard deviation is 13.0 points, find the 98% confidence interval of the true mean.
44.6 μ 64.0
Find x2 left and x2 right for a 95% confidence interval using the chi-square distribution with 14 degrees of freedom.
5.629, 26.119
Find x2 left and x2 right for a 99% confidence interval using the chi-square distribution with 17 degrees of freedom.
5.697, 35.718
Scores on the math SAT are normally distributed. A sample of 17 SAT scores had a standard deviation s=78. Construct a 95% confidence interval for the population standard deviation σ.
58.09 σ 118.71
A report states that 42% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4% with 95% confidence?
585
Scores on the math SAT are normally distributed. A sample of 23 SAT scores had a standard deviation s=79. Construct a 95% confidence interval for the population standard deviation σ.
61.10 σ 111.81
A researcher wants to construct a 90% confidence interval for the proportion of elementary school students in Seward County who receive free or reduced-price school lunches. A state-wide survey indicates that the proportion is 0.50. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.1?
68
Find x² left and x² right for a 90% confidence interval using the chi-square distribution with 15 degrees of freedom.
7.261, 24.996
Find x2 left and x2 right for a 99% confidence interval using the chi-square distribution with 20 degrees of freedom.
7.434, 39.997
What is the value for x² left for a 95% confidence interval when n=18?
7.564
5 squirrels were found to have an average weight of 8.8 ounces with a sample standard deviation is 0.9. Find the 95% confidence interval of the true mean weight.
7.7 μ 9.9
A study of 65 bolts of carpet showed that their average length was 74.2 yards. The standard deviation of the population is 3.6 yards. Which of the following is the 98% confidence interval for the mean length per bolt of carpet?
73.2 μ 75.2
A report states that 44% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 3% with 90% confidence?
746
A study of 55 apple trees showed that the average number of apples per tree was 825. The standard deviation of the population is 100. Which of the following is the 80% confidence interval for the mean number of apples per tree for all trees?
808 μ 842
A report states that 40% of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4 percentage points with 98% confidence?
815
A population has a standard deviation σ = 20.5. How large a sample must be drawn so that a 99% confidence interval for μ will have a margin of error equal to 5.4?
96
The term zα/2 (σ/√n) describes the ___________.
Maximum error of estimate.
Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal. 179, 168, 192, 125, 174, 200 Based on a 90% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 196? (Hint: you should first calculate the 90% confidence interval for the mean magnesium ion concentration.)
No.
In a study using 14 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is
a t distribution with 13 degrees of freedom.
In a study using 15 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is
a t distribution with 14 degrees of freedom.