Exam 7: Estimation: Single Population

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A clinic offers a weight-reduction program.A review of its records revealed the following weight losses,in pounds,for a random sample of 10 of its clients at the conclusion of the program: 20,15,21,28,22,19,9,14,18,and 23. -Find a point estimate of the population mean and population standard deviation of the weight losses.

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The quantity 100 (1 + α)% is called the confidence level of the interval.

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A 95% confidence interval estimate for a population mean μ is determined to be 65.48 to 76.52.Which of the following is true if a 90% confidence interval for μ is constructed?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A Monte Carlo study involves 10,000 random samples of size 20 from a normal population with mean μ = 120 and standard deviation σ = 20.For each sample,the mean and the median are calculated,with the following results: THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A Monte Carlo study involves 10,000 random samples of size 20 from a normal population with mean μ = 120 and standard deviation σ = 20.For each sample,the mean and the median are calculated,with the following results:    -Which of the two estimators appears most efficient? -Which of the two estimators appears most efficient?

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In a recent survey of 600 adults,16.4% indicated that they had fallen asleep in front of the television in the past month.Develop a 95% confidence interval for the population proportion.

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You are told that a 95% confidence interval for the population mean is 17.3 to 24.5.If the population standard deviation is 18.2,how large was the sample?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A school bus driver records the time (in minutes)it takes to commute to school for six days.Those results are: 25,22,17,20,15,and 10.Assuming the population is normally distributed,develop a 90% confidence interval for the population mean. -What is the value of the sample mean?

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If a sample of size 41 is selected,the value of A for the probability P(-A ≤ t ≤A)= 0.90 is:

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Which of the following distributions is used when estimating the population mean from a normal population with unknown variance?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following point estimators,W,X,Y,and Z of μ: W = (x1 + x2)/2; X = (2x1 + x2)/3;Y = (x1 + 3x2)/4;and Z = (2x1 + 3x2)/5. -Which of the following point estimators is the most efficient?

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The concept of margin of error is not applicable when estimating the population proportion P.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The Daytona Beach Tourism Commission is interested in the average amount of money a typical college student spends per day during spring break.They survey 35 students and find that the mean spending is $63.57 with a standard deviation of $17.32. -Develop a 95% confidence interval for the population mean daily spending.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that x1 and x2 are random samples of observations from a population with mean μ and variance σ2.Consider the following three point estimators,X,Y,and Z,of μ: X = (x1 + x2)/2,Y = (x1 + 3x2)/4,and Z = (x1 + 2x2)/3. -Which of the estimators X,Y,and Z is the most efficient?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let X1,X2,X3,and X4 be a random sample of observations from a population with mean μ and variance σ2.Consider the following two point estimators of μ: THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let X<sub>1</sub>,X<sub>2</sub>,X<sub>3</sub>,and X<sub>4</sub> be a random sample of observations from a population with mean μ and variance σ<sup>2</sup>.Consider the following two point estimators of μ:    <sub>1</sub> = 0.10 X<sub>1</sub> + 0.40 X<sub>2</sub> + 0.40 X<sub>3</sub> + 0.10 X<sub>4</sub> and    <sub>2</sub> = 0.20 X<sub>1</sub> + 0.30 X<sub>2</sub> + 0.30 X<sub>3</sub> + 0.20 X<sub>4</sub> -What is the relative efficiency of   <sub>1</sub> with respect to   <sub>2</sub>? 1 = 0.10 X1 + 0.40 X2 + 0.40 X3 + 0.10 X4 and THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let X<sub>1</sub>,X<sub>2</sub>,X<sub>3</sub>,and X<sub>4</sub> be a random sample of observations from a population with mean μ and variance σ<sup>2</sup>.Consider the following two point estimators of μ:    <sub>1</sub> = 0.10 X<sub>1</sub> + 0.40 X<sub>2</sub> + 0.40 X<sub>3</sub> + 0.10 X<sub>4</sub> and    <sub>2</sub> = 0.20 X<sub>1</sub> + 0.30 X<sub>2</sub> + 0.30 X<sub>3</sub> + 0.20 X<sub>4</sub> -What is the relative efficiency of   <sub>1</sub> with respect to   <sub>2</sub>? 2 = 0.20 X1 + 0.30 X2 + 0.30 X3 + 0.20 X4 -What is the relative efficiency of THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let X<sub>1</sub>,X<sub>2</sub>,X<sub>3</sub>,and X<sub>4</sub> be a random sample of observations from a population with mean μ and variance σ<sup>2</sup>.Consider the following two point estimators of μ:    <sub>1</sub> = 0.10 X<sub>1</sub> + 0.40 X<sub>2</sub> + 0.40 X<sub>3</sub> + 0.10 X<sub>4</sub> and    <sub>2</sub> = 0.20 X<sub>1</sub> + 0.30 X<sub>2</sub> + 0.30 X<sub>3</sub> + 0.20 X<sub>4</sub> -What is the relative efficiency of   <sub>1</sub> with respect to   <sub>2</sub>? 1 with respect to THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let X<sub>1</sub>,X<sub>2</sub>,X<sub>3</sub>,and X<sub>4</sub> be a random sample of observations from a population with mean μ and variance σ<sup>2</sup>.Consider the following two point estimators of μ:    <sub>1</sub> = 0.10 X<sub>1</sub> + 0.40 X<sub>2</sub> + 0.40 X<sub>3</sub> + 0.10 X<sub>4</sub> and    <sub>2</sub> = 0.20 X<sub>1</sub> + 0.30 X<sub>2</sub> + 0.30 X<sub>3</sub> + 0.20 X<sub>4</sub> -What is the relative efficiency of   <sub>1</sub> with respect to   <sub>2</sub>? 2?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: From a random sample of 500 registered voters in Los Angeles,400 indicated that they would vote in favor of a proposed policy in an upcoming election. -Calculate a 98% confidence interval estimate for the population proportion in favor of this policy.

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Like the standard normal distribution,all t - distributions have a mean of zero and a standard deviation of 1.

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If a sample of size 120 is selected,the value of A for the probability P(-A ≤ t ≤A)= 0.98 is:

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Whatever the value of the sample proportion, Whatever the value of the sample proportion,    (1 -    )cannot be smaller than 0.25. (1 - Whatever the value of the sample proportion,    (1 -    )cannot be smaller than 0.25. )cannot be smaller than 0.25.

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A random sample of size 15 is taken from a normally distributed population with a sample mean of 75 and a sample variance of 25.The upper limit of a 95% confidence interval for the population mean is equal to:

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The normal distribution is used to develop a confidence interval estimate of the population proportion if the sample size is large.

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