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Question
Let F be the event that a student is enrolled in afinance course, and let S be the event that a student is enrolled in a statistics course. It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and finance. Find the probability that a student is in finance and is also in statistics.a) 0.15
b) 0.70
c) 0.55
d) 0.12
e) 0.60
Answer
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Related questions
Q:
David Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. Based on a recent census of personnel, David knows that the variance of teller training time in the Southeast region is 8, and he wonders if the variance in the Southwest region is the same number. His staff randomly selected personnel files for 15 tellers in the Southwest Region, and determined that their mean training time was 25 hours and that the standard deviation was 4 hours. Assume that teller training time is normally distributed. Using = 0.10, the appropriate decision is ________.
a) increase the sample size
b) reduce the sample size
c) fail to reject the null hypothesis
d) maintain status quo
e) reject the null hypothesis
Q:
The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The appropriate decision is __________.
a) fail to reject the null hypothesis
b) reject the null hypothesis
c) reduce the sample size
d) increase the sample size
e) do nothing
Q:
The executives of CareFree Insurance, Inc. feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance. Eighty employees rate the management as participatory. The null hypothesis is __________.
a) n= 30
b) n= 200
c) p= 0.50
d) p< 0.50
e) n> 200
Q:
Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Using = 0.10, the critical zvalue is _______.
a) 1.645
b) -1.645
c) 1.28
d) -1.28
e) 2.28
Q:
A small restaurant owner believes at least 36 % of his customers would be willing to order take out service if it were available. He is interested in surveying his customer base. He intends to use the following null and alternative hypotheses.
Ho: p 0.36
Ha: p< 0.36
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
Q:
A small restaurant owner believes no more than 36 % of his customers travel over 10 miles to his business. He is interested in expanding his customer base through marketing. However, he would like to test his hypothesis prior to investing money in a marketing initiative. He intends to use the following null and alternative hypotheses.
Ho: p 0.36
Ha: p> 0.36
These hypotheses _______________.
a) indicate a one-tailed test with a rejection area in the right tail
b) indicate a one-tailed test with a rejection area in the left tail
c) indicate a two-tailed test
d) are established incorrectly
e) are not mutually exclusive
Q:
The weight of a USB flash drive is 30 grams and is normally distributed. Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives. If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues. The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively. Using = 0.10, the appropriate decision is _______.
a) reject the null hypothesis and shut down the process
b) reject the null hypothesis and do not shut down the process
c) fail to reject the null hypothesis and shut down the process
d) fail to reject the null hypothesis and do not shut down the processe) do nothing
Q:
A human resources analyst is developing a regression model to predict electricity production plant manager compensation as a function of production capacity of the plant, number of employees at the plant, and plant technology (coal, oil, and nuclear). The "plant technology" variable in this model is ______.
a) a response variable
b) a dependent variable
c) a quantitative variable
d) an independent variable
e) a constant
Q:
A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch), production plant (Kingsland, and Yorktown), and production shift (day, and evening). In this model, "shift" is ______.
a) a response variable
b) an independent variable
c) a quantitative variable
d) a dependent variable
e) a constant
Q:
The mean square error (MSerr) is calculated by dividing the sum of squares error (SSerr) by the number of error degrees of freedom (dferr).
Q:
Annie Mikhail, market analyst for a national company specializing in historic city tours, is analyzing the relationship between the sales revenue from historic city tours and the size of the city. She gathers data from six cities in which the tours are offered. Annie's dependent variable is annual sales revenues and her independent variable is the city population. Regression analysis of the data yielded the following tables. Coefficients
Standard Error
t Statistic
p-value Intercept
-0.14156
0.292143
-0.48455
0.653331 x
0.105195
0.013231
7.950352
0.001356 Source
df
SS
MS
F Se = 0.237 Regression
1
3.550325
3.550325
63.20809 r2 = 0.940483 Residual
4
0.224675
0.056169 Total
5
3.775 For a city with a population of 500,000, Annie's model predicts annual sales of ________________.
a) $70,780
b) $5,259
c) $170,780
d) $52,597
e) $152,597
Q:
Annie Mikhail, market analyst for a national company specializing in historic city tours, is analyzing the relationship between the sales revenue from historic city tours and the size of the city. She gathers data from six cities in which the tours are offered. Annie's dependent variable is annual sales revenues and her independent variable is the city population. Regression analysis of the data yielded the following tables. Coefficients
Standard Error
t Statistic
p-value Intercept
-0.14156
0.292143
-0.48455
0.653331 x
0.105195
0.013231
7.950352
0.001356 Source
df
SS
MS
F Se = 0.237 Regression
1
3.550325
3.550325
63.20809 r2 = 0.940483 Residual
4
0.224675
0.056169 Total
5
3.775 Annie's sample size is __________.
a) 2
b) 4
c) 6
d) 8
e) 10
Q:
Annie Mikhail, market analyst for a national company specializing in historic city tours, is analyzing the relationship between the sales revenue from historic city tours and the size of the city. She gathers data from six cities in which the tours are offered. Annie's dependent variable is annual sales revenues and her independent variable is the city population. Regression analysis of the data yielded the following tables. Coefficients
Standard Error
t Statistic
p-value Intercept
-0.14156
0.292143
-0.48455
0.653331 x
0.105195
0.013231
7.950352
0.001356 Source
df
SS
MS
F Se = 0.237 Regression
1
3.550325
3.550325
63.20809 r2 = 0.940483 Residual
4
0.224675
0.056169 Total
5
3.775 Annie's regression model can be written as: __________.
a) y = 7.950352 - 0.48455x
b) y = -0.48455 + 7.950352x
c) y = -0.14156 + 0.105195x
d) y = 0.105195 - 0.14156x
e) y = 0.105195 + 0.14156x
Q:
A manager wants to predict the cost (y) of travel for salespeople based on the number of days (x) spent on each sales trip. The following model has been developed: y = $400 + 120x. If a trip took 4 days, the predicted cost of the trip is _____________.
a) 480
b) 880
c) 524
d) 2080
e) 1080
Q:
In the regression equation, y=2.164+1.3657x n=6, the mean of x is 8.667, Sxx=89.333 and Se=3.44. A 95% prediction interval for y when x=8 is _________
a) (9.13, 17.05)
b) (2.75, 23.43)
c) (10.31, 15.86)
d) (3.56, 22.62)
e) (12.09, 14.09)
Q:
A researcher has developed a regression model from fourteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two"‘ tailed test and a = 0.01. The critical table t value is _______.
a) 2.650
b) 3.012
c) 3.055
d) 2.718
e) 2.168
Q:
In a regression analysis if SST = 200 and SSR = 200, r 2 = _________.
a) 0.25
b) 0.75
c) 0.00
d) 1.00
e) -1.00
Q:
The proportion of variability of the dependent variable accounted for or explained by the independent variable is called the _______.
a) sum of squares error
b) coefficient of correlation
c) coefficient of determination
d) covariance
e) regression sum of squares
Q:
The numerical value of the coefficient of determination must be _______.
a) between -1 and +1
b) between -1 and 0
c) between 0 and 1
d) equal to SSE/(n-2)
e) between -100 and +100
Q:
A standard deviation of the error of the regression model is called the _______.
a) coefficient of determination
b) sum of squares of error
c) standard error of the estimate
d) R-squared
e) coefficient of correlation
Q:
The following residuals plot indicates _______________. a) a nonlinear relation
b) a nonconstant error variance
c) the simple regression assumptions are met
d) the sample is biased
e) the sample is random
Q:
For the following scatter plot and regression line, at x = 35 the residual is _______.a) positiveb) zeroc) negatived) imaginarye) unknown
Q:
For a certain data set the regression equation is y = 29 - 5x. The correlation coefficient between y and x in this data set _______.
a) must be 0
b) is negative
c) must be 1
d) is positive
e) must be >1
Q:
Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc. (population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length. Recently, Stockton revised it rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s12= 0.15 with n1= 8, and, for Stockton, the results were s22= 0.05 with n2= 10. Assume that rod lengths are normally distributed in the population. If a= 0.05, the appropriate decision is _________.
a) reject the null hypothesis 12 = 22
b) reject the null hypothesis 12 < 22
c) do not reject the null hypothesis 12 = 22
d) do not reject the null hypothesis 12 < 22
e) do nothing
Q:
Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc. (population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length. Recently, Stockton revised it rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s12= 0.10 with n1= 8, and, for Stockton, the results were s22= 0.05 with n2= 10. Assume that rod lengths are normally distributed in the population If a= 0.05, the appropriate decision is ________.
a) reject the null hypothesis 12 = 22
b) reject the null hypothesis 12 < 22
c) do not reject the null hypothesis 12 = 22
d) do not reject the null hypothesis 12 < 22
e) do nothing
Q:
Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc. (population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length. Recently, Stockton revised it rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s12= 0.10 with n1= 8, and, for Stockton, the results were s22= 0.05 with n2= 10. Assume that rod lengths are normally distributed in the population. If a= 0.05, the critical Fvalue is _____________.
a) 3.68
b) 3.29
c) 3.50
d) 3.79
e) 3.99
Q:
A random sample of 400 items from a population shows that 160 of the sample items possess a given characteristic. A random sample of 400 items from a second population resulted in 110 of the sample items possessing the characteristic. Using this data, a 99% confidence interval is constructed to estimate the difference in population proportions which possess the given characteristic. The resulting confidence interval is _______.
a) 0.06 to 0.19
b) 0.05 to 0.22
c) 0.09 to 0.16
d) 0.04 to 0.21
e) 0.05 to 0.23
Q:
A researcher is interested in estimating the difference in two population proportions. A sample of 400 from each population results in sample proportions of .61 and .64. A 90% confidence interval for the difference in the population proportions is _______.
a) -0.10 to 0.04
b) -0.09 to 0.03
c) -0.11 to 0.05
d) -0.07 to 0.01
e) -0.08 to 0.12
Q:
Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Assuming = 0.05, the appropriate decision is ___________________.a) do not reject the null hypothesis 1- 2= 0b) do not reject the null hypothesis p1- p2= 0c) reject the null hypothesis 1- 2= 0d) reject the null hypothesis p1- p2= 0e) do not reject the null hypothesis p1- p20
Q:
Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Assuming a= 0.05, the observed zvalue is ___________________.
a) -3.15
b) 2.42
c) 1.53
d) 0.95
e) 1.08