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Exam 9: Estimating the Value of a Parameter

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Question 31

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Find the t-value such that the area in the right tail is 0.2 with 5 degrees of freedom.

A) 0.920
B) 0.200
C) -0.92
D) 0.941

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Question 32

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The area under the graph of every Studentʹs t-distribution is

A) 1
B) Less than the standard normal distribution
C) Greater than the standard normal distribution
D) $\frac { \text { Area of the standard normal distribution } } { \mathrm { s } / \sqrt { \mathrm { n } } }$ 3 Construct and interpret a confidence interval for a population mean.

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Question 33

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

The principal at Riverside High School would like to estimate the mean length of time each day that it takes allthe buses to arrive and unload the students. How large a sample is needed if the principal would like to assertwith 90% confidence that the sample mean is off by, at most, 7 minutes. Assume that s = 14 minutes based onprevious studies.

A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States thathas sleep deprivation. How large a sample is needed in order to be 95% confident that the sample proportionwill not differ from the true proportion by more than 4%?

True or False: As the level of confidence increases the number of item to be included in a sample will decreasewhen the error and the standard deviation are held constant.

Which of the following is not a characteristic of Studentsʹ t-distribution?

True or False? When constructing a (1 - α) 100% confidence interval for a population variance $\sigma ^ { 2 }$ thepopulation from which the random sample is selected can have any distribution.

A university dean is interested in determining the proportion of students who receive some sort of financialaid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receivingfinancial aid to within 1% with 90% reliability, how many students would need to be sampled?

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

Suppose a 90% confidence interval for μ turns out to be (1000, 2100) . If this interval was based on a sample ofsize n = 25, explain what assumptions are necessary for this interval to be valid.

Construct a 90% confidence interval for the population mean, μ. Assume the population has a normaldistribution. In a recent study of 22 eighth graders, the mean number of hours per week that they played videogames was 19.6 with a standard deviation of 5.8 hours. Round to the nearest hundredth.

Determine the sample size required to estimate the mean score on a standardized test within 4 points of thetrue mean with 98% confidence. Assume that s = 14 based on earlier studies.

A doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must sheselect if she desires to be 90% confident that her estimate is within 2 ounces of the true mean? Assume that s =5 ounces based on earlier studies.

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. Round tothe nearest cent.$3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00

Construct a 98% confidence interval for the population mean, μ. Assume the population has a normaldistribution. A study of 14 car owners showed that their average repair bill was $192 with a standard deviationof $8. Round to the nearest cent.

The June precipitation (in inches) for 10 randomly selected cities are listed below. Construct a 90% confidenceinterval for the population standard deviation, σ. Assume the data are normally distributed.2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

Find the critical t-value that corresponds to 95% confidence and n = 16.

Many people think that a national lobbyʹs successful fight against gun control legislation is reflecting the will ofa minority of Americans. A random sample of 4000 citizens yielded 2130 who are in favor of gun controllegislation. Find the point estimate for estimating the proportion of all Americans who are in favor of guncontrol legislation.