Question

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. Assuming that x1 and x2 have both been drawn independently from a population with mean μ and variance σ²
then which of the following is true...Which of the following point estimators is the most efficient?

• A. Z
• B. W
• C. X
• D. Y

An estimator is unbiased if the mean of its sampling distribution is the population parameter being estimated.

A. True B. False

A professor found that historically, the scores on the final exam tend to follow a normal distribution.  A random sample of nine test scores from the current class had a mean score of 187.9 points and a sample standard deviation of 32.4 points. Find the 90% confidence interval for the population mean score of the current class.

• A. [167.81, 207.99]
• B. [ 170.13 , 205.67]
• C. [ 166.73, 209.07]
• D. None of these answers are correct.

A taxi company is interested in the amount of time its vehicles are out of operation for repair. Find a 90% confidence interval for the mean number of days in a month that all taxis are out of operation for repair. A random sample of nine taxis had the following number of days that each was in repair (Note that we are using sample data and must estimate the sample standard deviation using the sample formula.):
10 16 19 14 19 21 22 8 17

A. 13.09 up to 19.35

• B. 12.54 up to 19.9

• C. 13.25 up to 19.19

• D. 12.24 up to 20.2

1. A random sample is obtained from a population with variance = 400 and the sample mean is computed to be 70. Consider the null hypothesis Ho: µ = 80 versus the alternative H1: Ho: µ < 80. Compute the p-value. If n = 16, the p-value is   .

Test Ho: µ =100; H1: µ < 100, using n = 36 and alpha = .05 If the sample mean = 95 and the sample standard deviation = 10, which of the following is true?

• A. test statistic = -3.00; critical value = -1.69; we fail to reject Ho.

• B. test statistic = -3.00; critical value = -1.69; we reject Ho and accept H1.

• C. test statistic = 3.00; critical value = 1.69; we reject Ho.

• D. None of these answers are correct.

Test Ho: µ =100; H1: µ < 100, using n = 36 and alpha = .05 If the sample mean = 95 and the sample standard deviation = 10, which of the following is true?

• A. test statistic = -3.00; critical value = -1.69; we fail to reject Ho.

• B. test statistic = -3.00; critical value = -1.69; we reject Ho and accept H1.

• C. test statistic = 3.00; critical value = 1.69; we reject Ho.

• D. None of these answers are correct.

Answer 1

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