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

Provide an appropriate response. -A container of soda is supposed to contain 1000 milliliters of soda. A quality control manager wants to be sure that the standard deviation of the soda containers is less than 20 milliliters. He randomly selects 10 cans of soda with a mean of 997 milliliters and a standard deviation of 32 milliliters. Use these sample results to construct a 95% confidence interval for the true value of . Does this confidence interval suggest that the variation in the soda containers is at an acceptable level

(Short Answer)

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Question 81

Find Critical Values for the Chi-Square Distribution -Find the critical values, $\chi _ { 1 } ^ { 2 } - \alpha / 2$ and $\chi _ { \alpha / 2 } ^ { 2 }$ , for $99 \%$ confidence and $n = 10$ .

(Multiple Choice)

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Question 82

Provide an appropriate response. -A survey of 500 non-fatal accidents showed that 141 involved faulty equipment. Find a point estimate for p. the population proportion of accidents that involved faulty equipment.

(Multiple Choice)

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Question 83

State the Properties of Student s t-Distribution -To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?

(Multiple Choice)

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Question 84

Construct and Interpret a Confidence Interval for a Pop Mean, Assuming that the Pop Std Dev is Known -In a recent study of 86 eighth graders, the mean number of hours per week that they played video games was 21.6. Assume $\sigma = 5.7$ hours. a) Compute the $90 \%$ confidence interval for $\mu$ . b) If the standard deviation is doubled to $11.4$ , what will be the effect on the confidence interval?

(Short Answer)

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Question 85

Provide an appropriate response. -A student randomly selects 10 paperbacks at a store. The mean price is $\$ 8.75$ with a standard deviation of $\$ 1.50$ . Construct a $95 \%$ confidence interval for the population standard deviation, $\sigma$ . Assume the data are normally distributed.

(Multiple Choice)

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Question 86

Choose the one alternative that best completes the statement or answers the question. -What statistical values does the margin of error depend upon

(Essay)

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Question 87

Write the word or phrase -Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight private colleges in the United States revealed the following endowments (in millions of dollars): $77.1,41.6,248.6,497.2,119,173.9,108.5$ , and $212.4$ . What value will be used as the point estimate for the mean endowment of all private colleges in the United States?

(Multiple Choice)

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Question 88

Choose the one alternative that best completes the statement or answers the question. -A group of 40 car owners calculated that their average repair bill was $\$ 192$ with a population standard deviation of $\$ 8$ . Compute the $95 \%$ confidence interval for the mean repair bill of all the owners.

(Multiple Choice)

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Question 89

Provide an appropriate response. -A survey of 2060 musicians showed that 301 of them are left-handed. Find a point estimate for p, the population proportion of musicians that are left-handed.

(Multiple Choice)

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Question 90

Provide an appropriate response. -A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normally distributed. Find the $95 \%$ confidence interval for the true mean.

(Multiple Choice)

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Question 91

Choose the one alternative that best completes the statement or answers the question. -A confidence interval for a parameter is

(Multiple Choice)

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Question 92

Find Critical Values for the Chi-Square Distribution -True or False: As the number of degrees of freedom increases, the chi-square distribution becomes more nearly symmetric.

(Multiple Choice)

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Question 93

Choose the one alternative that best completes the statement or answers the question. -A confidence interval with a 95% level of confidence means that the parameter will be in the interval for 95 out of 100 samples of the same size.

(True/False)

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Question 94

State the Properties of Student s t-Distribution -The area under the graph of every Student's t-distribution is

(Multiple Choice)

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Question 95

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error -A standardized test has a mean of 104 and a standard deviation of 16. We want to be 98% certain that we are within 4 points of the true mean. Determine the required sample size.

(Multiple Choice)

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Question 96

Determine t-values -Find the critical t-value that corresponds to $99 \%$ confidence and $\mathrm { n } = 10$ .

(Multiple Choice)

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Question 97

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error -A doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 98% confident that the true mean is within 2 ounces of the sample mean The standard deviation of the birth weights is known to be 8 ounces.

(Multiple Choice)

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Question 98

Provide an appropriate response. -Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a $95 \%$ confidence interval.

(Multiple Choice)

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Question 99

Explain the Role of Margin of Error in Constructing a Confidence Interval -Suppose a 90% confidence interval for turns out to be (120, 280). Based on the interval, do you believe the average is equal to 300

(Multiple Choice)

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Question 100

Showing 81 - 100 of 109

Find Critical Values for the Chi-Square Distribution -Find the critical values, $\chi _ { 1 } ^ { 2 } - \alpha / 2$ and $\chi _ { \alpha / 2 } ^ { 2 }$ , for $99 \%$ confidence and $n = 10$ .

Provide an appropriate response. -A survey of 500 non-fatal accidents showed that 141 involved faulty equipment. Find a point estimate for p. the population proportion of accidents that involved faulty equipment.

State the Properties of Student s t-Distribution -To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?

Provide an appropriate response. -A student randomly selects 10 paperbacks at a store. The mean price is $\$ 8.75$ with a standard deviation of $\$ 1.50$ . Construct a $95 \%$ confidence interval for the population standard deviation, $\sigma$ . Assume the data are normally distributed.

Choose the one alternative that best completes the statement or answers the question. -What statistical values does the margin of error depend upon

Choose the one alternative that best completes the statement or answers the question. -A group of 40 car owners calculated that their average repair bill was $\$ 192$ with a population standard deviation of $\$ 8$ . Compute the $95 \%$ confidence interval for the mean repair bill of all the owners.

Provide an appropriate response. -A survey of 2060 musicians showed that 301 of them are left-handed. Find a point estimate for p, the population proportion of musicians that are left-handed.

Provide an appropriate response. -A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normally distributed. Find the $95 \%$ confidence interval for the true mean.

Choose the one alternative that best completes the statement or answers the question. -A confidence interval for a parameter is

Find Critical Values for the Chi-Square Distribution -True or False: As the number of degrees of freedom increases, the chi-square distribution becomes more nearly symmetric.

Choose the one alternative that best completes the statement or answers the question. -A confidence interval with a 95% level of confidence means that the parameter will be in the interval for 95 out of 100 samples of the same size.

State the Properties of Student s t-Distribution -The area under the graph of every Student's t-distribution is

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error -A standardized test has a mean of 104 and a standard deviation of 16. We want to be 98% certain that we are within 4 points of the true mean. Determine the required sample size.

Determine t-values -Find the critical t-value that corresponds to $99 \%$ confidence and $\mathrm { n } = 10$ .

Explain the Role of Margin of Error in Constructing a Confidence Interval -Suppose a 90% confidence interval for turns out to be (120, 280). Based on the interval, do you believe the average is equal to 300

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

Find Critical Values for the Chi-Square Distribution -Find the critical values, χ12−α/2\chi _ { 1 } ^ { 2 } - \alpha / 2χ12​−α/2 and χα/22\chi _ { \alpha / 2 } ^ { 2 }χα/22​ , for 99%99 \%99% confidence and n=10n = 10n=10 .

Provide an appropriate response. -A survey of 500 non-fatal accidents showed that 141 involved faulty equipment. Find a point estimate for p. the population proportion of accidents that involved faulty equipment.

State the Properties of Student s t-Distribution -To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?

Choose the one alternative that best completes the statement or answers the question. -What statistical values does the margin of error depend upon

Provide an appropriate response. -A survey of 2060 musicians showed that 301 of them are left-handed. Find a point estimate for p, the population proportion of musicians that are left-handed.

Provide an appropriate response. -A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normally distributed. Find the 95%95 \%95% confidence interval for the true mean.

Choose the one alternative that best completes the statement or answers the question. -A confidence interval for a parameter is

Find Critical Values for the Chi-Square Distribution -True or False: As the number of degrees of freedom increases, the chi-square distribution becomes more nearly symmetric.

Choose the one alternative that best completes the statement or answers the question. -A confidence interval with a 95% level of confidence means that the parameter will be in the interval for 95 out of 100 samples of the same size.

State the Properties of Student s t-Distribution -The area under the graph of every Student's t-distribution is

Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error -A standardized test has a mean of 104 and a standard deviation of 16. We want to be 98% certain that we are within 4 points of the true mean. Determine the required sample size.

Determine t-values -Find the critical t-value that corresponds to 99%99 \%99% confidence and n=10\mathrm { n } = 10n=10 .

Explain the Role of Margin of Error in Constructing a Confidence Interval -Suppose a 90% confidence interval for turns out to be (120, 280). Based on the interval, do you believe the average is equal to 300

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

Find Critical Values for the Chi-Square Distribution -Find the critical values, $\chi _ { 1 } ^ { 2 } - \alpha / 2$ and $\chi _ { \alpha / 2 } ^ { 2 }$ , for $99 \%$ confidence and $n = 10$ .

Provide an appropriate response. -A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normally distributed. Find the $95 \%$ confidence interval for the true mean.

Determine t-values -Find the critical t-value that corresponds to $99 \%$ confidence and $\mathrm { n } = 10$ .