Exam 9: Estimating the Value of a Parameter Using Confidence Intervals

Provide an appropriate response. -A senator wishes to estimate the proportion of United States voters who favor abolishing the Electoral College. How large a sample is needed in order to be $98 \%$ confident that the sample proportion will not differ from the true proportion by more than $5 \%$ ?

(Multiple Choice)

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Question 41

Explain the Role of Margin of Error in Constructing a Confidence Interval -Suppose a 95% confidence interval for turns out to be (130, 300). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width

(Multiple Choice)

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Question 42

Provide an appropriate response. -In a college student poll, it is of interest to estimate the proportion $p$ of students in favor of changing from a quarter-system to a semester-system. How many students should be polled so that we can estimate p to within $0.09$ using a $99 \%$ confidence interval?

(Multiple Choice)

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Question 43

Provide an appropriate response. -How much money does the average professional hockey fan spend on food at a single hockey game? That question was posed to 10 randomly selected hockey fans. The sampled results show that sample mean and standard deviation were $\$ 19.00$ and $\$ 3.35$ , respectively. Use this information to create a $98 \%$ confidence interval for the mean.

(Multiple Choice)

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Question 44

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error - $\mathrm { E } = 4 , \sigma = 35 \text {, } ( 1 - \alpha ) = 0.90$

(Multiple Choice)

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Question 45

Choose the one alternative that best completes the statement or answers the question. -Determine the point estimate of the population mean for the confidence interval with a lower bound of 19 and an upper bound of 25 .

(Multiple Choice)

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Question 46

Provide an appropriate response. -A state highway patrol official wishes to estimate the number of legally intoxicated drivers on a certain road. a) How large a sample is needed in order to be $99 \%$ confident that the sample proportion will not differ from the true proportion by more than $2 \%$ ? b) Repeat part (a) assuming previous studies found that $80 \%$ of the drivers on this road are legally intoxicated.

(Short Answer)

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Question 47

Write the word or phrase that best completes each statement or answers the question. -The grade point averages for 10 randomly selected students in a statistics class with 125 students are listed below. What can you say about the mean score $\mu$ of all 125 students? 3.0 2.7 3.2 2.8 2.2 3.8 3.7 2.1 3.6 3.4

(Essay)

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Question 48

Determine t-values -Let to be a specific value of $t$ . Find $t _ { 0 }$ such that the following statement is true: $P \left( t \geq t _ { 0 } \right) = 0.1$ where $d f = 20$

(Multiple Choice)

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Question 49

Choose the one alternative that best completes the statement or answers the question. -A point estimate is the value of a_ that estimates the value of a_

(Multiple Choice)

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Question 50

Provide an appropriate response. -In a random sample of 26 laptop computers, the mean repair cost was $\$ 157$ with a standard deviation of $\$ 38$ . Assume the population has a normal distribution. a) Construct a $95 \%$ confidence interval for the population mean, $\mu$ . b) Suppose you did some research on repair costs for laptop computers and found that the standard deviation is $\sigma = 38$ . Use the normal distribution to construct a $95 \%$ confidence interval for the population mean, $\mu$ . Compare the results.

(Short Answer)

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Question 51

Provide an appropriate response. -Construct a $95 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. A sample of 20 part-time workers had mean annual earnings of $\$ 3120$ with a standard deviation of $\$ 677$ .

(Multiple Choice)

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Question 52

Provide an appropriate response. -A survey of 700 non-fatal accidents showed that 272 involved uninsured drivers. Construct a $99 \%$ confidence interval for the proportion of fatal accidents that involved uninsured drivers.

(Short Answer)

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Question 53

Provide an appropriate response. -The best point estimate for the standard deviation of a population is

(Multiple Choice)

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Question 54

State the Properties of Student s t-Distribution -Suppose a $99 \%$ confidence interval for $\mu$ turns out to be $( 1000,2100 )$ . If this interval was based on a sample of size $n = 26$ , explain what assumptions are necessary for this interval to be valid.

(Multiple Choice)

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Question 55

Choose the one alternative that best completes the statement or answers the question. -The margin of error of a confidence interval is

(Multiple Choice)

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Question 56

Provide an appropriate response. -The mean replacement time for a random sample of $12 \mathrm {~cd}$ players is $8.6$ years with a standard deviation of $5.1$ years. Construct the $98 \%$ confidence interval for the population variance, $\sigma ^ { 2 }$ . Assume the data are normally distributed

(Multiple Choice)

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Question 57

Provide an appropriate response. -What is the best point estimate for $p$ in order to construct a confidence interval for $p$ ?

(Multiple Choice)

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Question 58

Choose the one alternative that best completes the statement or answers the question. -A random sample of 56 lithium batteries has a mean life of 645 hours with a population standard deviation of 31 hours. Compute the $95 \%$ confidence interval for $\mu$ .

(Multiple Choice)

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Question 59

Provide an appropriate response. -Construct a $90 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. A sample of 15 randomly selected math majors has a grade point average of $2.86$ with a standard deviation of $0.78$ .

(Multiple Choice)

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Question 60

Showing 41 - 60 of 109

Provide an appropriate response. -A senator wishes to estimate the proportion of United States voters who favor abolishing the Electoral College. How large a sample is needed in order to be $98 \%$ confident that the sample proportion will not differ from the true proportion by more than $5 \%$ ?

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error - $\mathrm { E } = 4 , \sigma = 35 \text {, } ( 1 - \alpha ) = 0.90$

Choose the one alternative that best completes the statement or answers the question. -Determine the point estimate of the population mean for the confidence interval with a lower bound of 19 and an upper bound of 25 .

Determine t-values -Let to be a specific value of $t$ . Find $t _ { 0 }$ such that the following statement is true: $P \left( t \geq t _ { 0 } \right) = 0.1$ where $d f = 20$

Choose the one alternative that best completes the statement or answers the question. -A point estimate is the value of a_ that estimates the value of a_

Provide an appropriate response. -Construct a $95 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. A sample of 20 part-time workers had mean annual earnings of $\$ 3120$ with a standard deviation of $\$ 677$ .

Provide an appropriate response. -A survey of 700 non-fatal accidents showed that 272 involved uninsured drivers. Construct a $99 \%$ confidence interval for the proportion of fatal accidents that involved uninsured drivers.

Provide an appropriate response. -The best point estimate for the standard deviation of a population is

State the Properties of Student s t-Distribution -Suppose a $99 \%$ confidence interval for $\mu$ turns out to be $( 1000,2100 )$ . If this interval was based on a sample of size $n = 26$ , explain what assumptions are necessary for this interval to be valid.

Choose the one alternative that best completes the statement or answers the question. -The margin of error of a confidence interval is

Provide an appropriate response. -The mean replacement time for a random sample of $12 \mathrm {~cd}$ players is $8.6$ years with a standard deviation of $5.1$ years. Construct the $98 \%$ confidence interval for the population variance, $\sigma ^ { 2 }$ . Assume the data are normally distributed

Provide an appropriate response. -What is the best point estimate for $p$ in order to construct a confidence interval for $p$ ?

Choose the one alternative that best completes the statement or answers the question. -A random sample of 56 lithium batteries has a mean life of 645 hours with a population standard deviation of 31 hours. Compute the $95 \%$ confidence interval for $\mu$ .

Provide an appropriate response. -Construct a $90 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. A sample of 15 randomly selected math majors has a grade point average of $2.86$ with a standard deviation of $0.78$ .

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Distributions

Hypothesis Tests Regarding a Parameter

Inference on Two Samples

Inference on Categorical Data

Comparing Three or More Means

Inference of the Least-Squares Regression Model and Multiple Regression

Nonparametric Statistics

Filters

Exam 9: Estimating the Value of a Parameter Using Confidence Intervals

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error - E=4,σ=35, (1−α)=0.90\mathrm { E } = 4 , \sigma = 35 \text {, } ( 1 - \alpha ) = 0.90E=4,σ=35, (1−α)=0.90

Choose the one alternative that best completes the statement or answers the question. -Determine the point estimate of the population mean for the confidence interval with a lower bound of 19 and an upper bound of 25 .

Determine t-values -Let to be a specific value of ttt . Find t0t _ { 0 }t0​ such that the following statement is true: P(t≥t0)=0.1P \left( t \geq t _ { 0 } \right) = 0.1P(t≥t0​)=0.1 where df=20d f = 20df=20

Choose the one alternative that best completes the statement or answers the question. -A point estimate is the value of a_____ that estimates the value of a_____

Provide an appropriate response. -Construct a 95%95 \%95% confidence interval for the population mean, μ\muμ . Assume the population has a normal distribution. A sample of 20 part-time workers had mean annual earnings of $3120\$ 3120$3120 with a standard deviation of $677\$ 677$677 .

Provide an appropriate response. -A survey of 700 non-fatal accidents showed that 272 involved uninsured drivers. Construct a 99%99 \%99% confidence interval for the proportion of fatal accidents that involved uninsured drivers.

Provide an appropriate response. -The best point estimate for the standard deviation of a population is

State the Properties of Student s t-Distribution -Suppose a 99%99 \%99% confidence interval for μ\muμ turns out to be (1000,2100)( 1000,2100 )(1000,2100) . If this interval was based on a sample of size n=26n = 26n=26 , explain what assumptions are necessary for this interval to be valid.

Choose the one alternative that best completes the statement or answers the question. -The margin of error of a confidence interval is

Provide an appropriate response. -What is the best point estimate for ppp in order to construct a confidence interval for ppp ?

Choose the one alternative that best completes the statement or answers the question. -A random sample of 56 lithium batteries has a mean life of 645 hours with a population standard deviation of 31 hours. Compute the 95%95 \%95% confidence interval for μ\muμ .

Provide an appropriate response. -Construct a 90%90 \%90% confidence interval for the population mean, μ\muμ . Assume the population has a normal distribution. A sample of 15 randomly selected math majors has a grade point average of 2.862.862.86 with a standard deviation of 0.780.780.78 .

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

The Normal Probability Distribution

Sampling Distributions

Hypothesis Tests Regarding a Parameter

Inference on Two Samples

Inference on Categorical Data

Comparing Three or More Means

Inference of the Least-Squares Regression Model and Multiple Regression

Nonparametric Statistics

Filters

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error - $\mathrm { E } = 4 , \sigma = 35 \text {, } ( 1 - \alpha ) = 0.90$

Determine t-values -Let to be a specific value of $t$ . Find $t _ { 0 }$ such that the following statement is true: $P \left( t \geq t _ { 0 } \right) = 0.1$ where $d f = 20$

Choose the one alternative that best completes the statement or answers the question. -A point estimate is the value of a_ that estimates the value of a_

Provide an appropriate response. -Construct a $95 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. A sample of 20 part-time workers had mean annual earnings of $\$ 3120$ with a standard deviation of $\$ 677$ .

Provide an appropriate response. -A survey of 700 non-fatal accidents showed that 272 involved uninsured drivers. Construct a $99 \%$ confidence interval for the proportion of fatal accidents that involved uninsured drivers.

State the Properties of Student s t-Distribution -Suppose a $99 \%$ confidence interval for $\mu$ turns out to be $( 1000,2100 )$ . If this interval was based on a sample of size $n = 26$ , explain what assumptions are necessary for this interval to be valid.

Provide an appropriate response. -What is the best point estimate for $p$ in order to construct a confidence interval for $p$ ?

Choose the one alternative that best completes the statement or answers the question. -A random sample of 56 lithium batteries has a mean life of 645 hours with a population standard deviation of 31 hours. Compute the $95 \%$ confidence interval for $\mu$ .

Provide an appropriate response. -Construct a $90 \%$ confidence interval for the population mean, $\mu$ . Assume the population has a normal distribution. A sample of 15 randomly selected math majors has a grade point average of $2.86$ with a standard deviation of $0.78$ .