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Quantitive Analysis for Business 315*301 Test 3
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Terms in this set (28)
For statistical inference about the mean of a single population, the degrees of freedom for the t distribution equal n-1 because we lose one degree of freedom when we compute:
the sample mean
A study examined consumption of diesel and carbon dioxide emissions for a sample of counties.
Which of the following is the response variable in this study?
carbon dioxide emissions.
Suppose the correlation coefficient, r, between two variables is -0.44. What is the
corresponding R2?
0.19
The difference between correlation and regression analysis is that correlation measures the degree of association between two variables while regression examines causal relationship between two variables.
True
Based on data collected from automatic filling process of cheese ravioli, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. They find a sample mean weight of 15 grams. If the standard error of the mean is 0.3, what is the margin of error at 90% confidence?
0.5133
The regression line (fitted line) shows the predicted values of the dependent variable found by substituting the values of the independent/predictor variable in the estimated regression equation.
True
A correlation coefficient:
is always positive
is always negative
can never be zero
Correct
it can be positive, negative, or zero.
In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and a standard deviation of 0.65 feet. What is the 95% confidence interval for the true mean length of rods produced by this process?
95% confidence interval = mean± t
n-1 x SE(mean) = 14.8 ± t16-1, 0.05
* 0.65/sqr16 = 14.8 ± t15, 0.05 x 0.1625 = 14.8 ± 2.131 x 0.1625 =14.8±0.346 = 14.454 to 15.146.
A similar problem has been solved for you on page 20 of Ch. 11 ppts.
A plot of residuals is used to check which of the following?
if normality condition is satisfied
if linearity condition is satisfied
if equal spread condition is satisfied
Correct
all of the above.
The smaller the sum of the squared differences between the true value and the estimate of a parameter the better is the fit of the regression line to the data.
True
A company is interested in fostering good relationship with its local community. The company believes that at least 40% or more of its employees engage in community service activities. What are the correct null and alternative hypotheses to test this belief of the company?
HO: p = 0.40 and HA: p > 0.40
Computer chips manufacturing company finds that 8% of all chips manufactured are defective. In an effort to decrease the percentage of defective chips, management decides to provide additional training to its employees. After training was implemented, a sample of 450 chips revealed only 27 defects. What is the standard deviation of the sample proportion?
0.0128
If the p-value of a test statistic is 0.0039 and α = 0.05, then:
we would reject the null hypothesis
In a simple regression analysis, the standard error of the slope estimate (b1) of the regression line is equal to the true slope value of the parameter β1.
False
A supermarket chain gathers data on the amount they spend on promotional material and sales revenue generated each quarter. Which of the following is the predictor/explanatory variable?
amount spent on promotional material
Computer chips manufacturing company finds that 8% of all chips manufactured are defective. In an effort to decrease the percentage of defective chips, management decides to provide additional training to its employees. After training was implemented, a sample of 450 chips revealed only 27 defects. If the standard deviation of the sample proportion is 0.0128, which of the following is the value of the z - statistic?
-1.56
A small independent organic food store offers a variety of specialty coffees. To determine whether price of coffee has an impact on sales, the managers kept track of the pounds of each variety of coffee that were sold last month. Answer the following questions using the summary statistics given below.
= 8.75, = 54.50, r = -0.927, SD(x) = 3.63, SD(y) = 18.33.
a. What is the estimate of the slope parameter (b1)?
b. What is the estimate of the intercept term (b0)?
c. What is the estimated regression equation?
a. b1 = r.SD(y)/SD(x) = -0.927(18.33/3.63) = -0.927(5.050) = - 4.681.
b. b0 =- b1 = 54.50 - (-4.681)*8.75) = 54.50 + 40.95875 = 95.459
c. Estimate of y = ŷ = 95.459 - 4.681x.
A similar problem has been solved for you on page 24 of Ch 15 ppts.
If the standard error of the coefficient estimate (SEb1) = 1.20 and the t-stat (t-ratio) is 2.042, what is the slope coefficient estimate(b1) rounded to three decimal places?
2.450
When considering an action based on statistical results, a business decision-maker should take into account which of the following?
the statistical significance of the results
the cost of the proposed action
the size of the impact of the action (the effect size)
Correct
all of the above.
For a given value of x, the confidence interval for the predicted mean value of y is wider than the confidence interval for the predicted individual values of y.
False
Cars from an online service were examined to see how fuel efficiency (highway mpg) relates to cost (in dollars). According to the regression equation, a used car that costs $13,000 is predicted to get about 30.24 miles per gallon. According to actual data, the car got 35 miles per gallon. Based on this information, which of the following is the residual value?
4.76
A large correlation coefficient is a sign of causal relationship.
False
The residual is defined as the difference between the actual value of the dependent variable and its estimated value.
True
Suppose the actual value, the predicted value, and the residuals using a simple regression equation are as given below. What is the standard deviation of the residuals (se)?
y
ŷ
Residuals (e)
9
9.829
-0.829
8
8.531
-0.531
4
5.935
-1.935
3
2.041
0.959
10
8.531
1.469
12
11.127
0.873
Sum of squared residuals (e2) =(-0.829)2 + (-531)2 + (-1.935)2 + (0.959)2 + (1.469)2 + (0.873)2 = 8.553.
= √ 8.553/6-2 = √ 8.553/4 = 1.462.
GPA (grade point average) is believed to have a significant positive impact on the starting salary of college graduates. A regression model relating starting salary to GPA is specified as S = β0 + β1GPA + e, where, S is the annual starting salary in thousands and e is the error term. Estimation of this model using annual data of 10 randomly selected recent graduates produced the following regression statistics.
Variable
Coefficient Estimate
t-statistic
Intercept
15.310
3.896
GPA
6.745
3.412
Dependent Variable: Salary
n = 10, R2 = .85.
a. Is GPA a significant determinant of annual starting salary at 5% significance level? (Hint: Test HO: β1=0 vs HA: β1≠0 at α = 0.05).
b. Write the estimated regression equation.
c. According to this regression equation, what would be the starting annual salary of a graduate with 3.75 GPA?
d. What percent of the variation in the starting salary is not explained by this regression model?
a. To determine whether GPA is a significant determinant of starting annual salary, we compare the t-statistic of coefficient estimate b1 with the critical t-value for the DF of the model and the given significance level. If the t-stat is greater than the critical t-value, GPA is a significant determinant of annual starting salary.
The stat is 3.412 as given in the table above.
The critical t-value = t 0.05/2,= t 0.025, n-2 = t 0.025, 8 = 2.306 ( from t-dist. table)
Since 3.412 > 2.306, we reject the Ho and conclude that GPA is a significant determinant of salary.
b. Estimated regression equation = Ŝ = 15.310 + 6.745GPA
c. If GDA = 3.75;
Ŝ = 15.310 + 6.745(3.75) = 15.310 + 25.29 = $40.6 * 1000 = $40,600.
d. The percent of the variation in starting salary explained by this model is given by R2, which is 85% as given. The % of variation not explained is 1-0.85 = 15%.
When formulating a hypothesis test, the null and alternative hypotheses should be stated in terms of the:
population parameter.
The t distribution approaches the normal distribution as the sample size decreases.
False
Which of the following is the difference between the population regression equation and the estimated regression equation?
the error term is included in the population regression equation but is not
included in the estimated regression equation
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