The daily intakes of milk (in ounces) for ten five-year old children selected at random from one school were: \[\begin{array} { l l l l l } 21.7 & 27.9 & 12.2 & 25.7 & 16.9 \\ 17.7 & 12.2 & 31.1 & 14.0 & 28.0 \end{array}\] Find a 99% confidence interval for the standard deviation, ?, of the daily milk intakes of all five-year olds at this school. Round to the nearest hundredth when necessary.

A) (0.95, 3.51) B) (4.24, 14.50) C) (4.38, 14.50) D) (4.38, 16.14) A) (0.95, 3.51) B) (4.24, 14.50) C) (4.38, 14.50) D) (4.38, 16.14)

Exam 6: Inferences Based on a Single Sample: Estimation With Confidence Intervals

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the service industry is more than $1,500,000?

(Essay)

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Question 21

After elections were held, it was desired to estimate the proportion of voters who regretted that they did not vote. How many voters must be sampled in order to estimate the true proportion to within $2 \%$ (e.g., $\pm 0.02$ ) at the $90 \%$ confidence level? Assume that we believe this proportion lies close to $30 \%$ .

(Multiple Choice)

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Question 22

A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 95% confidence interval for the proportion of college students who prefer drink A: (.453, .493). Identify the point estimate for estimating the true proportion of college students who prefer that drink.

(Multiple Choice)

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Question 23

What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION $= .383277$ SAMPLE SIZE $= 159$ UPPER LIMIT $= .464240$ LOWER LIMIT $= .331153$ What proportion of the sampled students prefer foreign automobiles?

(Multiple Choice)

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Question 24

The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 49 different 24-hour periods and determines the number of admissions for each. For this sample, $\bar { x } = 17.2$ and $s ^ { 2 } = 25$ . Estimate the mean number of admissions per 24 -hour period with a $90 \%$ confidence interval.

(Multiple Choice)

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Question 25

A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following 90% confidence interval: (.438, .642). Based on the interval, is the population proportion of females equal to 48%?

(Multiple Choice)

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Question 26

A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects (60-year-old male non-smokers) and constructed the following 95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1050.00). Explain what the phrase "95 percent confident" means in this situation.

(Multiple Choice)

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Question 27

Suppose (1,000, 2,100) is a 95% confidence interval for µ. To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of $\mu _ { c }$

(Essay)

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Question 28

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). What assumption is necessary for the confidence interval analysis to work properly?

(Multiple Choice)

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Question 29

The standard deviation of a population is estimated to be 295 units. To estimate the population mean to within 46 units with 95% reliability, what size sample should be selected?

(Essay)

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Question 30

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.2%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

(Multiple Choice)

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Question 31

The confidence coefficient is the relative frequency with which the interval estimator encloses the population parameter when the estimator is used repeatedly a very large number of times.

(True/False)

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Question 32

The mean replacement time for a random sample of 12 CD players is 8.6 years with a standard deviation of 3.4 years. Construct the 99% confidence interval for the population variance, σ2. Assume the data are normally distributed, and round to the nearest hundredth when necessary.

(Multiple Choice)

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Question 33

The sampling distribution for $\hat{p}$ is approximately normal for a large sample size $n$ , where $n$ is considered large if both $n \hat { p } \geq 15$ and $n ( 1 - \hat { p } ) \geq 15$ .

(True/False)

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Question 34

We intend to estimate the average driving time of a group of commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 12 minutes. We wantour 99 percent confidence interval to have a margin of error of no more than plus or minus 3 minutes. What is the smallest sample size that we should consider?

(Multiple Choice)

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Question 35

The daily intakes of milk (in ounces) for ten five-year old children selected at random from one school were: 21.7 27.9 12.2 25.7 16.9 17.7 12.2 31.1 14.0 28.0 Find a 99% confidence interval for the standard deviation, ?, of the daily milk intakes of all five-year olds at this school. Round to the nearest hundredth when necessary.

(Multiple Choice)

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Question 36

What is $z _ { \alpha / 2 } \text { when } \alpha = 0.02 ?$

(Multiple Choice)

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Question 37

A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. A computer program was used to generate the following 95% confidence interval for the population proportion: (0.64814, 0.75186). Which of the following practical interpretations is correct for this confidence interval?

(Multiple Choice)

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Question 38

A random sample of 250 students at a university finds that these students take a mean of 14.3 credit hours per quarter with a standard deviation of 1.7 credit hours. The 95% confidence interval for the mean is 14.3 ± 0.211. Interpret the interval.

(Multiple Choice)

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Question 39

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for p is 59 ± .07. Interpret this interval.

(Multiple Choice)

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Question 40

Showing 21 - 40 of 135

A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following 90% confidence interval: (.438, .642). Based on the interval, is the population proportion of females equal to 48%?

Suppose (1,000, 2,100) is a 95% confidence interval for µ. To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of $\mu _ { c }$

The standard deviation of a population is estimated to be 295 units. To estimate the population mean to within 46 units with 95% reliability, what size sample should be selected?

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.2%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

The confidence coefficient is the relative frequency with which the interval estimator encloses the population parameter when the estimator is used repeatedly a very large number of times.

The mean replacement time for a random sample of 12 CD players is 8.6 years with a standard deviation of 3.4 years. Construct the 99% confidence interval for the population variance, σ2. Assume the data are normally distributed, and round to the nearest hundredth when necessary.

The sampling distribution for $\hat{p}$ is approximately normal for a large sample size $n$ , where $n$ is considered large if both $n \hat { p } \geq 15$ and $n ( 1 - \hat { p } ) \geq 15$ .

What is $z _ { \alpha / 2 } \text { when } \alpha = 0.02 ?$

A random sample of 250 students at a university finds that these students take a mean of 14.3 credit hours per quarter with a standard deviation of 1.7 credit hours. The 95% confidence interval for the mean is 14.3 ± 0.211. Interpret the interval.

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Exam 6: Inferences Based on a Single Sample: Estimation With Confidence Intervals

A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following 90% confidence interval: (.438, .642). Based on the interval, is the population proportion of females equal to 48%?

Suppose (1,000, 2,100) is a 95% confidence interval for µ. To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of μc\mu _ { c }μc​

The standard deviation of a population is estimated to be 295 units. To estimate the population mean to within 46 units with 95% reliability, what size sample should be selected?

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.2%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

The confidence coefficient is the relative frequency with which the interval estimator encloses the population parameter when the estimator is used repeatedly a very large number of times.

The mean replacement time for a random sample of 12 CD players is 8.6 years with a standard deviation of 3.4 years. Construct the 99% confidence interval for the population variance, σ2. Assume the data are normally distributed, and round to the nearest hundredth when necessary.

The sampling distribution for p^\hat{p}p^​ is approximately normal for a large sample size nnn , where nnn is considered large if both np^≥15n \hat { p } \geq 15np^​≥15 and n(1−p^)≥15n ( 1 - \hat { p } ) \geq 15n(1−p^​)≥15 .

What is zα/2 when α=0.02?z _ { \alpha / 2 } \text { when } \alpha = 0.02 ?zα/2​ when α=0.02?

A random sample of 250 students at a university finds that these students take a mean of 14.3 credit hours per quarter with a standard deviation of 1.7 credit hours. The 95% confidence interval for the mean is 14.3 ± 0.211. Interpret the interval.

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Suppose (1,000, 2,100) is a 95% confidence interval for µ. To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of $\mu _ { c }$

The sampling distribution for $\hat{p}$ is approximately normal for a large sample size $n$ , where $n$ is considered large if both $n \hat { p } \geq 15$ and $n ( 1 - \hat { p } ) \geq 15$ .

What is $z _ { \alpha / 2 } \text { when } \alpha = 0.02 ?$