Bus. Stats. Test 3
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. At a 5% significance level, the critical value(s) is(are) ________. a. 1.645 b. 1.690 c. -1.96 and 1.96 d. -2.030 and 2.030
a. 1.645
Costco sells paperback books in their retail stores and wanted to examine the relationship between price and demand. The price of a particular novel was adjusted each week and the weekly sales were recorded in the following table. Sales Price 7 $12 4 $11 5 $10 9 $9 8 $8 8 $7 7 $7 Management would like to use simple regression analysis to estimate weekly demand for this novel using the price of the novel. The total sum of squares for this sample is equal to ________. a. 18.86 b. 21.56 c. 22.86 d. 26.93
a. 18.86
Which of the following is not true of the standard error of the estimate? a. It can take on negative values. b. Theoretically, its value has no predefined upper limit. c. It is a measure of the accuracy of the regression model. d. It is based on the squared deviations between the actual and predicted values of the response variable.
a. It can take on negative values.
Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type I error is often referred to as ___________. a. a false positive b. a false negative c. a negative result d. the power of the test
a. a false positive
A company has developed a new diet that it claims will lower one's weight by more than 10 pounds. Health officials decide to conduct a test to validate this claim. The consumers should be _____________________________________. a. more concerned about Type I error b. more concerned about Type II error c. concerned about both Type I and Type II errors d. is not concerned at all
a. more concerned about Type I error
A correlation coefficient r = −0.85 could indicate a __________________. a. very weak positive linear relationship b. very strong negative linear relationship c. very weak negative linear relationship d. very strong positive linear relationship
b. very strong negative linear relationship
Consider the following sample regression equation formula185.mml = 150 - 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of the good increases by $3, then we expect demand for Product A to ______________. a. increase by 60 b. decrease by 60 c. decrease by 60,000 d. increase by 60,000
c. decrease by 60,000
Over the past 30 years, the sample standard deviations of the rates of return for stock X and sStock Y were 0.20 and 0.12, respectively. The sample covariance between the returns of X and Y is 0.0096. The correlation of the rates of return between X and Y is the closest to ____. a. 0.20 b. 0.24 c. 0.36 d. 0.40
d. 0.40
Consider the sample regression equation y-hat=100 + 10x, with an R2 value of 0.81. Which of the following is the value of the sample correlation between y and y-hat? a. −0.90 b. −0.81 c. 0.81 d. 0.90
d. 0.90
When estimating formula246.mml = β0 + β1x1 + β2x2 + ε, the following regression results using ANOVA were obtained. df SS MS F Regression 2 210.9 105.5 114.7 Residual 1 7 15.6 0.92 Total 1 9 2 26.5 C Coe SE t-stat p-value Inter. −1.6 0.57 −2.77 0.0132 x1 −0.5 0.04 −15.11 2.77E-11 x2 0.1 0.07 1.89 0.0753 Which of the following is the standard error of the estimate? a. 0.82 b. 0.86 c. 0.92 d. 0.96
d. 0.96
Which of the following statements is the least accurate concerning correlation analysis? a. Correlation does not imply causation. b. The correlation coefficient captures only a linear relationship. c. The correlation coefficient may not be a reliable measure when outliers are present in one or the both of the variables. d. The correlation coefficient describes both the direction and strength of the relationship between two variables only if the two variables have the same units of measurement.
d. The correlation coefficient describes both the direction and strength of the relationship between two variables only if the two variables have the same units of measurement.
When two regression models applied on the same data set have the same response variable but a different number of explanatory variables, the model that would evidently provide the better fit is the one with a __________. a. lower standard error of the estimate and a higher coefficient of determination b. higher standard error of the estimate and a higher coefficient of determination c. higher coefficient of determination and a lower adjusted coefficient of determination d. lower standard error of the estimate and a higher adjusted coefficient of determination
d. lower standard error of the estimate and a higher adjusted coefficient of determination
When conducting a hypothesis test, which of the following decisions represents an error? a. Rejecting the null hypothesis when it is true. b. Rejecting the null hypothesis when it is false. c. Not rejecting the null hypothesis when it is true. d. Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true.
a. Rejecting the null hypothesis when it is true.
Consider the following data: 1formula21.mml = 20, sx = 2, 1formula22.mml = -5, sy = 4, and b1 = -0.8. The sample correlation coefficient, rxy is equal to ____. a. −0.40 b. −0.20 c. 0.20 d. 0.40
a. −0.40
The sample standard deviations for x and y are 10 and 15, respectively. The covariance between x and y is −120. The correlation coefficient between x and y is _____. a. −0.8 b. −0.5 c. 0.5 d. 0.8
a. −0.8
A retailer is looking to evaluate its customer service. Management has determined that if the retailer wants to stay competitive, then it will have to have at least a 93% satisfaction rate among its customers. Management will take corrective actions if the satisfaction rate falls below 93%. A survey of 1,250 customers showed that 1,150 were satisfied with their customer service.
a. Select the hypotheses to test if the retailer needs to improve its services. H0: p ≥ 0.93; HA: p < 0.93 b. What is the value of the test statistic? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Test statistic -1.39 c. The p-value is: (Round p-value to 4 decimal places.) 0.05 Picture p-value < 0.10 d. At α = 0.10, what is the conclusion? The management will take corrective action
The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest? a. The mean score on the eighth-grade reading comprehension test b. The number of eighth graders who took the reading comprehension test c. The standard deviation of the score on the eighth-grade reading comprehension test d. The proportion of eighth graders who scored above 73 on the reading comprehension test
a. The mean score on the eighth-grade reading comprehension test
For a given sample size n, _____________________. a. decreasing the probability of a Type I error α will increase the probability of a Type II error β b. decreasing the probability of a Type I error α will decrease the probability of a Type II error β c. changing the probability of a Type I error α will have no impact on the probability of a Type II error β d. increasing the probability of a Type I error α will increase the probability of a Type II error β as long as σ is known
a. decreasing the probability of a Type I error α will increase the probability of a Type II error β
When we reject the null hypothesis when it is actually false, we have committed _________. a. no error b. a Type I error c. a Type II error d. a Type I error and a Type II error
a. no error
A one-tailed hypothesis test of the population mean has ______________. a. only one critical value b. two critical values, both positive c. two critical values, both negative d. two critical values, one positive and one negative
a. only one critical value
An analyst conducts a hypothesis test to check whether the mean return for a particular fund differs from 10%. He assumes that returns are normally distributed and sets up the following competing hypotheses: Ho:μ = 10,HA:μ ≠ 10 Over the past 10 years the fund has had an average annual return of 13.4% with a standard deviation of 2.6%. The value of the test statistic is 4.14 and the critical values at the 5% significance level are−2.262 and 2.262.The correct decision is to ____________________________________. a. reject Ho; we can conclude that the mean differs from 10% b. reject Ho; we cannot conclude that the mean differs from 10% c. not reject Ho; we can conclude that the mean differs from 10% d. not reject Ho; we cannot conclude that the mean differs from 10%
a. reject Ho; we can conclude that the mean differs from 10%
A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. At a 5% significance level, the decision is to ____________________.. a. reject Ho; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 b. reject Ho; we cannot conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 c. not reject Ho; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 d. not reject Ho; we cannot conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20
a. reject Ho; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20
A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $5,600. He takes a random sample of 16 of the new salesperson's sales and finds an average markup of $5,000 and a standard deviation of $800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim? a. t15 = -3.00 b. z = -3.00 c. t15 = -0.75 d. z = -0.75
a. t15 = -3.00
The standard error of the estimate measures ______________. a. the standard deviation of the residuals. b. the standard deviation of the response variable. c. the standard deviation of the explanatory variable. d. the standard deviation of the correlation coefficient.
a. the standard deviation of the residuals.
If the chosen significance level is α = 0.05, then ____________________________________________. a. there is a 5% probability of rejecting a true null hypothesis b. there is a 5% probability of accepting a true null hypothesis c. there is a 5% probability of rejecting a false null hypothesis d. there is a 5% probability of accepting a false null hypothesis
a. there is a 5% probability of rejecting a true null hypothesis
The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The p-value for this hypothesis test would be ______. a. 0.1310 b. 0.0950 c. 0.0475 d. 0.0219
b. 0.0950
The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The p-value for this hypothesis test would be ______. a. 0.1310 b. 0.0950 c. 0.0475 d. 0.0219a
b. 0.0950
In the estimation of a multiple regression model with two explanatory variables and 20 observations, SSE = 550 and SST = 1000. Which of the following is the correct value of R2? a. 0.10 b. 0.45 c. 0.55 d. 0.90
b. 0.45
Which of the following Excel's functions return the correlation coefficient? a. CORRELATION b. CORREL c. CORREL.S d. COVARIANCE.S
b. CORREL
It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. Identify the correct null and alternative hypotheses to test the politician's claim. a. H0:p = 0.50 and HA:p ≠ 0.50 b. H0:p ≤ 0.50 and HA:p > 0.50 c. H0:p ≥ 0.50 and HA:p > 0.50 d. H0:p ≥ 0.50 and HA:p < 0.50
b. H0:p ≤ 0.50 and HA:p > 0.50
Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200. Which of the following hypothesis tests should be performed? a. Left-tailed b. Right-tailed c. Two-tailed d. There is not enough information to answer.
b. Right-tailed
Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type II error is often referred to as ___________. a. a false positive b. a false negative c. a negative result d. the power of the test
b. a false negative
The alternative hypothesis typically ___________. a. corresponds to the presumed default state of nature b. contests the status quo, for which a corrective action may be required c. states the probability of rejecting the null hypothesis when it is false d. states the probability of rejecting the null hypothesis when it is true
b. contests the status quo, for which a corrective action may be required
A company has developed a new diet that it claims will lower one's weight by more than 10 pounds. Health officials decide to conduct a test to validate this claim. The manager of the company _____________________________________. a. is more concerned about Type I error b. is more concerned about Type II error c. is concerned about both Type I and Type II errors d. is not concerned at all
b. is more concerned about Type II error
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The parameter to be tested is ___________________________. a. the mean GPA of all university students b. the mean GPA of the university honors students c. the mean GPA of 3.60 for the 36 selected honors students d. the proportion of honors students with a GPA exceeding 3.50
b. the mean GPA of the university honors students
Consider the following simple linear regression model: y = β0 + β1x + ε. The explanatory variable is ____. a. y b. x c. ε d. β0
b. x
Consider the following data: 1formula34.mml = 20, sx = 2, 1formula35.mml = -5, sy = 4, and b1 = 0.40. Which of the following is the sample regression equation? a. y-hat=-13-0.40x b. y-hat=-13+0.40x c. y-hat=3-0.40x d. y-hat=3+0.40x
b. y-hat=-13+0.40x
The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later, School Buses Still Late," Boston Globe, October 5, 2011). Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 12 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement—students were not as late. Assume a population standard deviation for bus arrival time of 12 minutes.The value of the test statistic is ____________. a. t35 = -2.00 b. z = -2.00 c. t35 = -0.33 d. z = -0.33
b. z = -2.00
Which of the following are two-tailed tests? a. Ho:μ ≤ 10, HA:μ > 10 b. Ho:μ = 10, HA:μ ≠ 10 c. Ho:μ ≥ 400, HA:μ < 400 d. Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400
b.Ho:μ = 10, HA:μ ≠ 10
The following table shows the number of cars sold last month by six dealers at Centreville Nissan dealership and their number of years of sales experience. Years of Experience Sales 1 7 2 9 2 9 4 8 5 14 8 14 Management would like to use simple regression analysis to estimate monthly car sales using the number of years of sales experience. The slope of the regression equation is equal to _______. a. −3.33 b. 0.71 c. 1.00 d. 6.15
c. 1.00
Costco sells paperback books in their retail stores and wanted to examine the relationship between price and demand. The price of a particular novel was adjusted each week and the weekly sales were recorded in the following table. Sales Price 7 $12 4 $11 5 $10 9 $9 8 $8 8 $7 7 $7 Management would like to use simple regression analysis to estimate weekly demand for this novel using the price of the novel. The average weekly sales for the novel when priced at $10 is equal to ________. a. 4.60 b. 5.07 c. 6.45 d. 7.33
c. 6.45
What type of data would necessitate using a hypothesis test of the population proportion rather than a test of the population mean? a. Ratio b. Interval c. Qualitative d. Quantitative
c. Qualitative
When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the ______________________________________. a. probability of Type II error decreases b. probability of incorrectly rejecting the null hypothesis increases c. probability of incorrectly accepting the null hypothesis increases d. probability of incorrectly accepting the null hypothesis decreases
c. probability of incorrectly accepting the null hypothesis increases
A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. The value of the test statistic is ___________. a. t35 = -2.40 b. z = -2.40 c. t35 = 2.40 d. z = 2.40
c. t35 = 2.40
The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. The population parameter to be tested is ___________. a. the average number of 750 customers per day b. the proportion of customers visiting the dealership per day c. the mean number of customers visiting the dealership per day d. the standard deviation of the number of customers visiting the dealership per day
c. the mean number of customers visiting the dealership per day
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The value of the test statistic is ____________. a. z = -1.50 b. t35 = -1.50 c. z = 1.50 d. t35 = 1.50
c. z = 1.50
Consider the following simple linear regression model: y = β0 + β1x + ε. The random error term is ____. a. y b. x c. ε d. β0
c. ε
Consider the following sample regression equation formula195.mml = 200 + 10x, where y is the supply for Product A (in 1000s)(in 1,000s) and x is the price of Product A (in $). If the price of Product A is $5, then we expect supply to be _____. a. 250 b. 2,500 c. 25,000 d. 250,000.
d. 250,000.
Which of the following are one-tailed tests? a. Ho:μ ≤ 10, HA:μ > 10 b. Ho:μ = 10, HA:μ ≠ 10 c. Ho:μ ≥ 400, HA:μ < 400 d. Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400
d. Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400
A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86].At the 1% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0? a. Reject Ho; we can conclude that the mean differs from zero. b. Reject Ho; we cannot conclude that the mean differs from zero. c. Do not reject Ho; we can conclude that the mean differs from zero. d. Do not reject Ho; we cannot conclude that the mean differs from zero.
d. Do not reject Ho; we cannot conclude that the mean differs from zero.
Which of the following identifies the range for a correlation coefficient? a. Any value less than 1. b. Any value greater than 0. c. Any value between 0 and 1. d. None of these choices is correct.
d. None of these choices is correct.
Which of the following types of tests may be performed? a. Right-tailed and two-tailed tests b. Left-tailed and two-tailed tests c. Right-tailed and left-tailed tests d. Right-tailed, left-tailed, and two-tailed tests
d. Right-tailed, left-tailed, and two-tailed tests
The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The confidence interval for this hypothesis test would be __________________. a. [$14,118.9, $19,881.2] b. [$14,839.1, $19,160.9] c. [$16,279.7, $17,720.3] d. [$15,588.2, $18,411.8]
d. [$15,588.2, $18,411.8]
Consider the following competing hypotheses: Ho:μ = 0, HA:μ ≠ 0. The value of the test statistic is z = −1.38. If we choose a 5% significance level, then we ___________________________________________. a. reject the null hypothesis and conclude that the population mean is significantly different from zero b. reject the null hypothesis and conclude that the population mean is not significantly different from zero c. do not reject the null hypothesis and conclude that the population mean is significantly different from zero d. do not reject the null hypothesis and conclude that the population mean is not significantly different from zero
d. do not reject the null hypothesis and conclude that the population mean is not significantly different from zero
Consider the following sample regression equation formula191.mml= 200 + 10x, where y is the supply for Product A (in 1000s)(in 1,000s) and x is the price of Product A (in $). The slope coefficient indicates that if ___________. a. the price of Product A increases by $1, then on average, supply decreases by 10 b. the price of Product A increases by $1, then on average, supply increases by 10 c. the price of Product A increases by $1, then on average, supply decreases by 10,000 d. the price of Product A increases by $1, then on average, supply increases by 10,000
d. the price of Product A increases by $1, then on average, supply increases by 10,000