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MCQS & Hypothesis Testing
For all calculation questions (#25 - 42), provide detailed calculations. All confidence interval problems should be set-up in their proper format. For all hypothesis tests, you should state the null and alternative hypotheses that you are testing. For problems involving looking up values off a table, indicate which probability distribution table was used and what value you were seeking
(1) Suppose we divide a group of 750 cows by five breeds and then randomly select 10 cows from each group and test them on their milk production. What type of sampling is this?
(a) Simple Random
(b) Clustered Random
(c) Stratified Random
(d) Systematic Random
(e) Stratified Non-random __________
(2) As the number of samples increase, the standard error associated with the sample means
(a) Increases
(b) Decreases
(c) Remains unchanged
(d) Can increase, decrease or remain unchanged
(e) Is irrelevant __________
(3) For a population not normally distributed, as the size of the sample gets larger, the distribution of the sample means will
(a) be negatively skewed
(b) approach the normal distribution
(c) take the shape of the population distribution
(d) be positively skewed
(e) None of the above __________
(4) A large number (but not all) possible samples of size `n` are selected from a population and the mean of each sample is determined. What is the mean of the sample means?
(a) Exactly the same as the population mean
(b) Slightly larger than the population mean
(c) Slightly smaller than the population mean
(d) Cannot be determined in advance
(e) None of the above are correct __________
(5) An experiment involves selecting a random sample of 30 salaries from 256 middle managers for study. The sample mean is computed to be $35,420, the sample mode is $34,500, the sample median is $35,165 and the sample standard deviation is $2,050. What is the point estimate of the population salary mean?
(a) $33,165
(b) $2,050
(c) $35,420
(d) $34,500
(e) None of the above are correct __________
(6) An interval estimate is a range of values used to estimate
(a) the shape of the population`s distribution
(b) the sampling distribution
(c ) a sample statistic
(d) a population parameter
(e) None of the above are correct _________
(7) For the interval estimation of when is not known and the sample is large, the proper distribution to use is
(a) the normal distribution
(b) the t distribution with n degrees of freedom
(c) the t distribution with n - 1 degrees of freedom
(d) the t distribution with n - 2 degrees of freedom
(e) None of the above are correct __________
(8) A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to 0.90 (all else remains the same), the interval for
(a) becomes narrower
(b) becomes wider
(c) does not change
(d) becomes 0.1
(e) None of the above are correct __________
(9) In hypothesis testing, the hypothesis tentatively assumed to be true is
(a) the alternative hypothesis
(b) the null hypothesis
(c) either the null or the alternative
(d) None of these alternatives is correct. __________
(10) The level of significance is the
(a) maximum allowable probability of Type II error
(b) maximum allowable probability of Type I error
(c ) same as the confidence coefficient
(d) same as the p-value
(e) None of the above is true __________
(11) In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been found to be true,
(a) a Type I error has been committed
(b) a Type II error has been committed
(c) either a Type I or Type II error has been committed
(d) the correct decision has been made __________
(12) When the p-value is used for hypothesis testing, the null hypothesis is rejected if
(a) p-value <
(b) < p-value
(c) p-value >
(d) p-value =
(e) None of the above is true __________
(13) Which of the following is not true?
(a) For a given sample size, if the Type I error increases, the Type II error will decrease
(b) For a given sample size, if the Type II error decreases, the Type I error will increase
(c) Its possible to reduce both error types simultaneously by increasing the sample size
(d) The p-value gives the level of significance where on either side a hypothesis will be either accepted or rejected
(e) All of the above are true __________
(14) Which of the following is not true regarding the covariance between two variables?
(a) Is a measures of linear association between the variables
(b) Is a bounded measure
(c) Is used in calculating the correlation coefficient
(d) Can take on the value 0
(e) All of the above are true __________
(15) Correlation analysis is used to determine
(a) the equation of the regression line
(b) a specific value of the dependent variable for a given value of the independent variable
(c ) the strength of the relationship between the dependent and the independent variables
(d) None of these alternatives is correct. __________
(16) Which of the following is not true if r = -1.00?
(a) Dependent variable can be perfectly predicted by the independent variable
(b) None of the variation in the dependent variable can be accounted for by the independent variable
(c ) High values of one variable are associated with low values of the other variable
(d) All of the above are true __________
(17) What does a coefficient of correlation of 0.80 mean?
(a) Almost no correlation between two variables
(b) Coefficient of determination is 0.64
(c ) 80% of the variation in one variable is explained by the other
(d) Coefficient of nondetermination is 0.20
(e) None of the above __________
(18) In regression analysis, which of the following is not a required assumption about the error term?
(a) The expected value of the error term is zero.
(b) The variance of the error term is the same for all values of X.
(c) The values of the error term are independent.
(d) The values of the independent variables are independent of the error terms.
(e) All are required assumptions __________
(19) Application of the least squares regression method results in values of the y intercept and the slope which minimizes the sum of the squared deviations between the
(a) observed values of the independent variable and the estimated values of the independent variable
(b) actual values of the independent variable and estimated values of the dependent variable
(c) observed values of the dependent variable and estimated values of the independent variable
(d) observed values of the dependent variable and the estimated values of the dependent variable
(e) None of these alternatives is correct. __________
(20) Larger values of R2 imply that the observations are more closely grouped about the
(a) average value of the independent variables
(b) mean value of the dependent variable
(c) regression line
(d) origin
(e) None of these alternatives is correct. __________
(21) In multiple regression analysis,
(a) there can be any number of dependent variables but only one independent variable
(b) there must be only one independent variable
(c ) the coefficient of determination must be larger than 1
(d) there can be several dependent variables and several independent variables
(e) None of these alternatives is correct. __________
(22) The regression error most commonly associated with time series data is called:
(a) multicollinearity
(b) homoscedacticity
(c) heteroscedacticity
(d) auto-correlation
(e) None of the above __________
(23) A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called
(a) an interaction
(b) a constant variable
(c) a dummy variable
(d) None of these alternatives is correct __________
(24) When the assumption that the error terms of a regression model do not exhibit the same variance, what condition is present?
(a) multicollinearity
(b) homoscedacticity
(c) heteroscedacticity
(d) auto-correlation
(e) None of the above __________
(25) A random sample of 81 automobiles traveling on an interstate showed an average speed of 60 mph and a standard deviation of 13.5 mph. The 86.9% confidence interval for is
(a) 46.500 to 73.500
(b) 57.735 to 62.265
(c) 59.131 to 60.869
(d) 50 to 70
(e) None of the above __________
(26) The mean weight of trucks traveling on the Virginia section of I-495 is not known. A state highway inspector needs an estimated mean. He selects 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 3.8 tons. Using the 0.95 degree of confidence, what is the confidence interval within which the population mean lies?
(a) 14.7 and 16.9
(b) 13.2 and 17.6
(c) 10.3 and 20.4
(d) 16.1 and 18.1
(e) None of the above __________
(27) In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation is 1.2 hours. If the sample mean is 9 hours, then the 95% confidence interval is
(a) 7.04 to 10.96 hours
(b) 7.36 to 10.64 hours
(c) 7.80 to 10.20 hours
(d) 8.74 to 9.26 hours
(e) None of the above __________
(28) The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. At the 5% significance level, it can be concluded that the mean of the population is
(a) significantly greater than 3
(b) not significantly greater than 3
(c) significantly less than 3
(d) significantly greater then 3.18
(e) None of the above __________
(29) A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly different from 24. At the 5% significance level, it can be concluded that the mean age is
(a) not significantly different from 24
(b) significantly different from 24
(c) significantly less than 24
(d) significantly less than 25
(e) None of the above __________
(30) In the following intercorrelation matrix, which variables exhibit multi-collinearity? Use a .70 cutoff value in answering.
X1 X2 X3 X4
X1 1.0 .67 .45 .65
X2 .67 1.0 .73 .60
X3 .45 .73 1.0 .75
X4 .65 .60 .75 1.0
(a) (X1 and X2) and (X2 and X4)
(b) (X1 and X3) and (X1 and X4)
(c ) (X1 and X2) and (X2 and X3)
(d) (X2 and X3) and (X3 and X4)
(e) (X1, X3 and X4) __________
(31) In a regression analysis if SST=4500 and SSE=3600, then the coefficient of determination is
(a) 0.20
(b) 0.40
(c) 0.60
(d) 0.80
(e) None of these alternatives is correct. __________
(32) A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation
= 20,000 - .5X
The above equation implies that an
(a) increase of $1 in price is associated with a decrease of $.50 in sales
(b) increase of $8 in price is associated with an increase of $500 in sales
(c) increase of $1 in price is associated with a decrease of $50 in sales
(d) increase of $1 in price is associated with a decrease of $500 in sales
(e) None of these alternatives is correct. __________
(33) What is the adjusted Coefficient of Determination given the following multiple regression data:
Sum of Squares Regression = 2500 Sum of Squares Error = 1500
Number of observations = 21 Number of independent variables = 10
(a) 25%
(b) 37.5%
(c) 62.5%
(d) 75%
(e) None of the above __________
(34) In a study of foreign holdings in the U.S. banks, year-end share of assets in U.S. bank subsidiaries held by foreigners (as a percentage of total assets) was related to:
X1 = Annual change, in billions of dollars, in foreign direct investment in the U.S. (excluding finance, insurance, and real estate);
X2 = Bank price-earnings ratio;
X3 = Index of the exchange value of the dollar.
The regression results from the sample data gave the following population parameter estimates:
a = -2.256 b1= .201 b2= -.144 b3=.032 R2=.89
What is the estimated year-end share of assets in U.S. bank subsidiaries held by foreigners for a particular year if the annual change in foreign direct investment in the U.S., (excluding finance, insurance, and real estate) was $20 Billion, the bank price-earnings ratio was 15, and the index of exchange value of the dollar was 155?
(a) 3.456
(b) 4.564
(c) 6.138
(d) 12.097
(e) None of the above is correct __________
(35) Below you are given computer output from a multiple regression model based on a sample of 25 observations.
Coefficient Standard Error
Constant 145.321 48.682
X1 25.625 9.150
X2 5.720 3.575
X3 0.823 0.183
Test whether the parameter 1 is significant at the 5% significance level. The null hypothesis should be
a. rejected
b. not rejected
c. revised
d. None of these alternatives is correct. __________
(36) A quality control technician is checking the weights (lbs) of a particular product. She takes a random sample of 8 units and weighs each unit. The observed weights (lbs) are shown below.
Weight
50
48
55
52
53
46
54
50
Compute a 95% confidence interval for the mean weight of all units.
(37) You are the benefits and compensation director for a company. You have a national medical insurance plan for your company`s employees which provides for either 100% of the usual and customary rates for a variety of surgical procedures or the actual charge, whichever is lower. You retain the records of the actual charges by procedure, and for most surgical procedures the average actual charge is close to the usual and customary rate defined by the insurer. You have noticed a discrepancy, however, between the average actual charge and customary rate for childbirths by Caesarean section. The usual customary rate is at $1,200 and the average of the actual charges based on a sample of 32 cases is only $1,150 with a sample standard deviation of $300. You are concerned about discrepancies in both directions. Since your insurance fees are experience-rated, if the usual and customary rates were set too high, your company would be paying too much. If the insurer`s usual and customary rates were set too low, your employees might view their compensation package as inadequate. Test at the 5% significance level whether there is a problem with the customary rate.
Show your work here:
(a) What is the null and alternative hypotheses?
(b) Work through the hypothesis test.. What conclusion do you reach?
© What is the p-value?
(38) In one of the efforts to maintain internal control on sales, the auditor for the Saxon Plumbing Company takes a sample on invoices at the end of the month to evaluate the mean amount listed on the sales invoices for the warehouse in that month. Over the past five years, the mean amount per sales invoice for customers outside the suburban area in which Saxon is located is $120. Because shipping costs are affected by delivery distance, it is important that the auditor carefully monitor the mean sales amount. The following data are the amounts (in dollars) in a random sample of 12 sales invoices that were selected from the population of sales invoices for customers outside the suburban area during the past month:
109.98 152.22 111.45 110.59 127.46 107.26 93.32 91.97 111.56 75.71 128.58 135.11
(a) State the null and alternative hypothesis to be test whether or not there has been a change in the mean sales invoice amount for customers outside the suburban area serviced by Saxon (1 point)
(b) Perform the appropriate test at a 5% significance level and state your conclusion in non-statistical language (i.e., what does your acceptance or rejection of your null hypothesis tell management)
(c ) What is the p-value associated with the sample results?
(39) A sales manager for a steam cleaning equipment company believes there is a relationship between the population of a city and the amount of sales. To verify this belief, the following data was collected:
City Population (millions) Sales ($ millions)
1 2.0 $3.0
2 1.0 1.0
3 1.5 2.0
4 0.5 0.8
5 1.5 3.0
6 1.0 1.5
7 3.0 5.0
8 2.0 4.0
What is the regression equation ?
What is the value of coefficient of determination?
(40) The following data show the results of a study of a sample of 14 stores to estimate the annual sales of stores (`000$) based upon their size (square feet).
Store $ Sales (000) Sq. Ft.
1 3,681 1,726
2 3,895 1,642
3 6,653 2,816
4 9,543 5,555
5 3,418 1,292
6 5,563 2,208
7 3,660 1,313
8 2,694 1,102
9 5,468 3,151
10 2,898 1,516
11 10,674 5,161
12 7,585 4,567
13 11,760 5,841
14 4,085 3,008
a. Develop a least squares estimated regression line.
b. Compute the coefficient of determination.
(41) Sponsors of a local charity decided to attract wealthy patrons to its $500-a-plate dinner by allowing each person to buy a set of 20 tickets for the gaming tables. The chance of winning a prize for each of the 20 plays was 50-50. If you bought 20 tickets, what is the chance of winning 15 or more prizes?
(42) The production department has installed a new spray gun to paint automobile doors. As common with most spray guns, unsightly blemishes often appear because of improper mixture or other problems. The average number of blemishes is 0.5 per door. If the distribution of blemishes follows a poisson distribution, out of 10,000 doors painted, about how many would have no blemishes ?
See attached file.
All solutions/answers should appear in doc file as well, though calculations can be done in excel.