Answer this question (question 17) and questions 18 and 19 on the basis of the following regression results, standard errors in parentheses, n = 200)
Qd = -500 - 100Pa + 50Pb + .3I + .2A
(250) (50) (30) (.1) (.08)
R2 = .12
Where Qd = 10,500 quantity demanded of product "A"
Pa = $10, price of product "A"
Pb = $8, price of product "B"
I = $12,000 per capita income
A = $20,000 monthly advertising expenditure
1. Which of the Variables does NOT pass the t-test at the .05 level of significance?
e. All the variables pass the t-test
2. As a researcher, which aspect of the results would be of greatest concern?
a. The negative value of the constant (i.e., -500)
b. The relatively low impact of the competitor's price
c. The fact that not all of the variables are statistically significant
d. The poor fit of the regression line
3. As the manager of Product A, which of the following would be of greatest concern (based on the regression results above)?
a. None of the factors below would be of concern.
b. An impending recession.
c. Pressure on you by your salespersons to lower the price so that they can boost their sales.
d. A price reduction by the makers of product B.
4. Among the advantages of the least-squares trend analysis techniques is
a. The ease of calculation.
b. Relatively little analytical skill required.
c. Its ability to provide information regarding the statistical significance of the results.
d. All of the above
The solution gives answers to multiple choice questions on least squares estimation. The questions are related to regression equation, Student's t-test, least squares estimation, slope, intercept, correlation, residual, R square, coefficient of determination and regression coefficients.
Statistics - Multiple Choice: estimation, z value, confidence interval, t statistic, point estimate for population proportion, error of the estimation, point estimate of the population variance, chi-square values, sample size
Question 1: When a statistic calculated from sample data is used to estimate a population parameter, it is called :
an interval estimate
a point estimate
a statistical parameter
a good guess
Question 2: A large appliance company sends out technicians to unpack, assemble, and connect every gas dryer that is sold. In developing a pricing strategy, it is important to the company to have a "handle" on how long this process takes. The company hires a research assistant to follow technicians on 45 randomly selected jobs. The research assistant records how much time it takes the technicians to unpack, assemble, and connect each gas dryer. The resulting sample mean is 34.3 minutes. If research assistant concludes based on the sample mean that the average time for all such jobs is 34.3 minutes she is using a:
a range estimate
a statistical parameter
an interval estimate
a point estimate
Question 3: The Z value associated with a two sided 90% confidence interval is:
Question 4: Suppose a random sample of 36 is selected from a population with a standard deviation of 12. If the sample mean is 98, the 99% confidence interval to estimate the population mean is:
94.08 to 101.92
97.35 to 98.65
92.85 to 103.15
93.34 to 102.66
Question 5: What is the average length of a wireless phone call? Suppose researchers in the telecommunications industry want to estimate the average number of minutes of a wireless call. To do so, they randomly select one such call from 85 wireless phone bills around the country. The resulting sample mean is 2.54 minutes with a standard deviation of 1.20 minutes. From these data, the 86% confidence interval to estimate the average length of a wireless phone call for all users is:
2.285 to 2.795
2.326 to 2.754
2.347 to 2.733
2.519 to 2.561
Question 6: The t statistic was developed by:
Question 7: In order to find values in the t distribution table, you must convert the sample size or sizes to:
degrees of freedom
Question 8: A researcher is taking a random sample of 18 items in an effort to estimate the population mean. He wants to be 95% confident of his results. The table t value that he should use is:
Question 9: A researcher is interested in estimating the mean value for a population. She takes a random sample of 17 items and computes a sample mean of 224 and a sample standard deviation of 32. She decides to construct a 98% confidence interval to estimate the mean. Assuming that the population is normally distributed, the resulting confidence interval is:
219.138 to 228.862
204.077 to 243.923
203.953 to 244.047
207.546 to 240.454
Question 10: The weights of aluminum castings produced by a process are normally distributed. A random sample of 5 castings is selected; the sample mean weight is 2.21 pounds; and the sample standard deviation is 0.12 pound. The 99% confidence interval for the population mean casting weight is:
2.009 to 2.411
2.100 to 2.320
1.825 to 2.595
1.963 to 2.457
Question 11: A researcher wants to estimate the proportion of the population which possess a given characteristic. A random sample of size 600 is taken resulting in 276 items which possess the characteristic. The point estimate for this population proportion is _______.
Question 12: A researcher wants to estimate the proportion of the population that possesses a given characteristic using a 90% confidence interval. A random sample of size 600 is taken resulting in 330 items that possess the characteristic. The error of the estimation of the confidence interval is:
Question 13: To estimate the proportion of a population that possesses a given characteristic, a random sample of 1700 people are interviewed from the population. Seven hundred and fourteen of the people sampled possess the characteristic. Using this information, the researcher computes an 88% confidence interval to estimate the proportion of the population who possess the given characteristic. The resulting confidence interval is:
.401 to .439
.409 to .431
.392 to .448
.389 to .451
Question 14: From a sample of 42 items, a company wants to estimate the proportion of the population that is defective. Using the results of the sample given below, construct a 96% confidence interval to estimate that proportion. In the data below, a "y" denotes a defect.
.685 to .934
.049 to .332
.066 to .314
.072 to .309
Question 15: If a researcher is calculating a confidence interval and increases the confidence then the width of the confidence interval will do what, all other things being constant?
Remain the same
None of the above
Question 16: The relationship of the sample variance to the population variance is captured by which distribution?
Question 17: A researcher wants to estimate the population variance. He is certain that the population is normally distributed. In an effort to construct a confidence interval, he randomly selects eight members of the population. The data are shown below. What is the point estimate of the population variance?
Question 18: A financial officer wants to estimate the population variance of daily deposits at the bank. The officer randomly records 14 deposits. The sample mean deposit is $235 with a sample standard deviation of $42. In estimating the population variance from these data, what is the point estimate?
Question 19: A researcher wants to construct a 99% confidence interval to estimate a population variance using a random sample of 13 observations. The chi-square values for this confidence interval are:
Question 20: A fund manager manages a portfolio of 250 common stocks. The manager relies on various statistics, such as variance, to assess the overall risk of stocks in an economic sector. The manager's staff reported that for a sample 12 utility stocks the mean annualized return was 14% and that the variance was 3%. The 95% confidence interval for the population variance of annualized returns is
1.41 to 7.49
1.68 to 7.21
1.51 to 8.65
4.52 to 25.95
Question 21: In determining the sample size necessary to estimate a population mean, the error of estimation, E, is equal to
the distance between the sample mean and the population mean
the distance between the sample mean and the variance
the z score
the sample size
Question 22: In determining the sample size necessary to estimate p, if there is no good approximation for the value of p available, then what value should be used as an estimate of p in the formula?
Question 23: A researcher wants to estimate the average diameter of the population of a three foot long pipe. The researcher wants to be within .1" of the actual average and be 90% confident. The population variance of diameters for this type pipe is .25. How large of a sample size should be taken?
Question 24: A business researcher wants to estimate the proportion of all workers who feel stressed out with their job. The researcher is certain that the proportion is no more .22. She wants to be 99% confident of the results and be within .04 of the true population proportion. She needs to sample at least:
Question 25: A researcher with a large national chain of fast food restaurants wants to estimate the proportion of customers who order French fries with their hamburger. The researcher is uncertain about what the proportion may actually be, wants to be 95% confident about the results, and wants to be within .03 of the actually figure. The researcher needs to sample at least: