Final quiz for Quantitative Methods -- Download Full Solution : Click HERE
1.
A sample of eight observations of variables x and y is shown below:
x 5 3 7 9 2 4 6 8
y 20 23 15 11 27 21 17 14
Find the value of coefficient of correlation, r.
(Points: 6)
- 0.991
0.872
- 0.512
0.942
2. The largest value in a set of data is 160, and the smallest value is 70. If the resulting frequency distribution is to have six classes of equal width, what will be the class interval? (Points: 6)
15
6
12
5
3. Chebyshev�s Theorem states that the percentage of observations in a data set that should fall within five standard deviations of their mean is: (Points: 6)
90%
at least 90%
96%
at least 96%
25%
4.
The salaries (in thousands of dollars) for a sample of 13 employees of a firm are: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
Compute the variance of the salaries.
(Points: 6)
2.562
6.125
9.223
7.097
5. A monthly report to the Texas Department of Health, division of Water Hygiene, contained the following water production data in thousands of gallons:
5263 5636 5264 4395 6090 5293 4668 5725 5171 4378
5118 5538 4838 5167 5119 5438 6843 5262 4653 5303
5913 4570 5142 5964 6431 4719 5358 6043 4554 5805
What is the value of the interquartile range. The values are rounded (no decimal values included). (Points: 6)
A) 937
B) 752
C) 886
D) 912
6. Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates� years of experience are as follows.
Candidate Experience
Female 1
Female 2
Female 3
Male 1
Male 2
Male 3 5
9
11
6
4
8
Suppose one of the candidates is selected at random. Define the following events:
A = person selected has 9 years experience
B = person selected is a female
Find P(A / B). (Points: 6)
A) 0.4552
B) 0.333
C) 0.581
D) 0.418
7. For a normally distributed random variable, the average price for a bushel of soybeans is $6.20 with a standard deviation of $0.20.
For what proportion of outcomes will the price be between $6.10 and $6.30? (Points: 6)
A) 0.2015
B) 0.4458
C) 0.3252
D) 0.3830
8. A pharmaceutical company interested in measuring how often physicians prescribe a certain drug has selected a simple random sample from each of two groups: M.D. (medical doctors) and D.O (osteopathic doctors). What is this type of sampling called? (Points: 6)
Simple random sampling
Cluster sampling
Stratified sampling
Purposive sampling
9.
The odds in favor of an event are the number of successes divided by the number of failures. The probability of this event occurring is the number of successes divided by the sum of the number of successes and the number of failures. The number of successes is five and the number of failures is four.
Find the odds in favor of success.
(Points: 6)
5 to 9
4 to 9
5 to 4
4 to 5
10. Approximately 14 percent of the population of Arizona is 65 years or older. A random sample of five persons from this population is taken. The probability that less than 2 of the 5 are 65 years or older is (Points: 6)
0.8533
0.1467
0.4704
0.3829
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11. In the past, young women drivers have maintained a better driving record than young men drivers. An insurance company is concerned with the driving record of its insured customers. Specifically, it conducts a test for the number of speeding tickets received during the past year by drivers between the ages of 18 and 25.
Men Women
n1= 120 n2= 85
1= 1.2
2 = 0.4
s21 = 24.8 s22 = 10.6
A test for the equality of average number of tickets per driver for the two groups is desired.
Use = 0.01.
Calculate the p-value for this test.
(Points: 6)
A) 0.3395
B) 0.2015
C) 0.1646
D) 0.4561
12. Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, exceeds 78 is (Points: 6)
0.4332
0.0668
0.0987
0.9013
13. A producer of a juice drink advertises that it contains 10% real fruit juices. A sample of 75 bottles of the drink is analyzed and the percent of real fruit juices is found to be 6.5%. If the true proportion is actually 0.10, what is the probability that the sample percent will be 6.5% or less? (Points: 6)
0.7211
0.1562
0.5488
0.8325
14. The security department of a state university is planning its budget for the next year. In estimating the man-hours for security during university sponsored music concerts, the average length of music concerts is needed. A random sample from thirty-six security departments at universities was taken and the sample mean length of concerts was 160 minutes. Suppose the population standard deviation is 45 minutes. A 95 percent confidence interval for the true mean duration of music concerts is: (Points: 6)
157.55 to 162.45
147.63 to 172.37
71.8 to 248.2
145.3 to 174.7
15. Based on sample data, the 90% confidence interval limits for the population mean are 170.86 and 195.42. If the 10% level of significance was used in testing the hypotheses : =201, : 201, the null hypothesis: (Points: 6)
would be rejected
would not be rejected
would have to be revised
None of the above
16. Suppose that 9 observations are drawn from a normal population whose standard deviation is 2. The observations are: 15, 9, 13, 11, 8, 12, 11, 7, and 10. At 95% confidence, you want to determine whether the mean of the population from which this sample was taken is significantly different from 10.
Compute the value of the test statistic and interpret the result. (Points: 6)
A) Z= 1.5; reject H0
B) Z =1.0; fail to reject H0
C) Z=1.0; reject H0
D) Z= 1.5; fail to reject
17.
Consider the following data values of variables x and y:
x 97 113 81 68 90 79
y 103 103 105 115 127 104
Use Excel to perform a regression analysis on the data. What is the regression equation?
(Points: 6)
A) Y = 12 � 1.54 X
B) Y = 83 + 38.28 X
C) Y= 125 � 0.173 X
D) Y = 98 + 0.115 X
18. The number of degrees of freedom associated with the t test, when the data are gathered from a matched pairs experiment with 13 pairs, is: (Points: 6)
13
26
12
24
19. One-way ANOVA is performed on three independent samples with: = 6, = 7, and = 8. The critical value obtained from the F-table for this test at the 2.5% level of significance equals: (Points: 6)
3.55
39.45
4.56
29.45
20. A multiple regression analysis includes 25 data points and 4 independent variables results in SST = 200 and SSR = 150. The multiple standard error of estimate will be: (Points: 6)
1.333
6.124
2.500
1.581
21. Membership on a stock exchange for five years is given below:
Year Members
1996 520
1997 510
1998 505
1999 508
2000 512
Use the exponential smoothing procedure to obtain estimates of the trend (this is not the logarithm approach here).
Set the smoothed value for 1996 equal to the actual and use a smoothing constant,
α = 0.4. Compute the forecasted value for 2000.
(Points: 6)
A) 510.896
B) 437.246
C) 635.324
D) 310.775
22. The upsurge in school supply sales in the fall of each year is an example of the: (Points: 6)
irregular component.
trend component.
seasonal component.
cyclical component.
23. When the purpose of sampling is to detect when a process becomes too variable, the chart of choice will be a c-chart. Is it true or false? (Points: 6)
True
False
24. Forty samples of size 1,000 were drawn from a manufacturing process and the number of defectives in each sample was counted. The mean sample proportion was 0.05. The centerline for the p chart is: (Points: 6)
0.05
50.0
2.00
25.0
25. A Type II error is defined as: (Points: 6)
rejecting a true null hypothesis
rejecting a false null hypothesis
failing to reject a true null hypothesis
failing to reject a false null hypothesis
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