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Total Points: 100 points
Instruction: You can type or hand-write your answers. Please indicate clearly the question numbers. In the free response questions and data analysis questions, please show steps of calculation or detailed explanation. You are free to choose any software package in the data analysis questions. But be sure to present the machine outputs in human readable formats.
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I. Multiple Choices or Fill in the Blank (30 points in total, 2 points for each question)
1. The expected value of equals the mean of the population from which the sample is drawn
a. only if the sample size is 30 or greater
b. only if the sample size is 50 or greater
c. only if the sample size is 100 or greater
d. for any sample size
2. The standard deviation of a point estimator is the
a. standard error
b. sample statistic
c. point estimate
d. sampling error
3. The value of the is used to estimate the value of the population parameter.
a. population statistic
b. sample parameter
c. population estimate
d. sample statistic
4. A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained.
12 18 19 20 21
A point estimate of the population mean is
a. 5
b. 18
c. 19
d. 20
5. The sampling distribution of the sample mean
a. is the probability distribution showing all possible values of the sample mean
b. is used as a point estimator of the population mean μ
c. is an unbiased estimator
d. shows the distribution of all possible values of μ
6. As the sample size increases, the variability among the sample means
a. increases
b. decreases
c. remains the same
d. depends upon the specific population being sampled
7. Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 196. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are
a. 180 and 24.39
b. 180 and 28
c. 180 and 1.74
d. 180 and 2
8. In determining an interval estimate of a population mean when σ is unknown, we use a t distribution with
a. degrees of freedom
b. degrees of freedom
c. n - 1 degrees of freedom
d. n degrees of freedom
9. Random samples of size 36 are taken from a process (an infinite population) whose mean and standard deviation are 20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample mean are
a. 36 and 15
b. 20 and 15
c. 20 and 0.417
d. 20 and 2.5
10. The fact that the sampling distribution of the sample mean can be approximated by a normal probability distribution whenever the sample size is large is based on the
a. central limit theorem
b. fact that there are tables of areas for the normal distribution
c. assumption that the population has a normal distribution
d. All of these answers are correct.
11. It is known that the variance of a population equals 1,936. A random sample of 121 has been taken from the population. There is a .95 probability that the sample mean will provide a margin of error of
a. 7.84 or less
b. 31.36 or less
c. 344.96 or less
d. 1,936 or less
12. From a population that is normally distributed with an unknown standard deviation, a sample of 25 elements is selected. For the interval estimation of μ, the proper distribution to use is the
a. standard normal distribution
b. z distribution
c. t distribution with 26 degrees of freedom
d. t distribution with 24 degrees of freedom
13. A random sample of 25 employees of a local company has been measured. A 95% confidence interval estimate for the mean systolic blood pressure for all company employees is 123 to 139. Which of the following statements is valid?
a. 95% of the sample of employees has a systolic blood pressure between 123 and 139.
b. If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
c. 95% of the population of employees has a systolic blood pressure between 123 and 139.
d. If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139.
14. The general form. of an interval estimate of a population mean or population proportion is the plus and minus the .
a. population mean, standard error
b. level of significance, degrees of freedom
c. point estimate, margin of error
d. planning value, confidence coefficient