Business analytics final exam (9-10

Regression analysis was applied between sales (in $1000s) and advertising (in $100s), and the following regression function was obtained. ​ y = 500 + 4x ​ Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is _____.

$900,000

The critical F value with 6 numerator and 60 denominator degrees of freedom at α = .05 is _____.

2.25

As a general guideline, the research hypothesis should be stated as the _____.

alternative hypothesis

In regression and correlation analysis, if SSE and SST are known, then with this information the _____.

coefficient of determination can be computed

In the ANOVA, treatment refers to _____.

different levels of a factor

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called _____.

the regression model

The t distribution should be used whenever _____.

the sample standard deviation is used to estimate the population standard deviation

The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to _____.

.50

If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be _____.

.9

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is _____.

.95

The mean of the t distribution is _____.

0

The degrees of freedom for a contingency table with 6 rows and 3 columns is _____.

10

The degrees of freedom for a contingency table with 12 rows and 12 columns is _____.

121

In an analysis of variance problem involving three treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is _____.

14.8

The t value with a 95% confidence and 24 degrees of freedom is _____.

2.064

The z value for a 97.8% confidence interval estimation is _____.

2.29

A random sample of 36 students at a community college showed an average age of 25 years. Assume the ages of all students at the college are normally distributed with a standard deviation of 1.8 years. The 98% confidence interval for the average age of all students at this college is _____.

24.301 to 25.699

An ANOVA procedure is used for data that were obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are _____.

3 and 16

The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both p̄ and n(1 - p) equal or exceed _____.

5

If the correlation coefficient is .8, then the percentage of variation in the dependent variable explained by the estimated regression equation is _____.

64%

In a completely randomized design involving three treatments, the following information is provided: Treatment 1 Sample size- 5 Sample mean- 4 Treatment 2 Sample size- 10 Sample mean- 8 Treatment 3 Sample size- 5 Sample mean- 9 ​ The overall mean for all the treatments is _____.

7.25

Excel's _____ function is used to perform a goodness of fit test.

CHISQ.TEST

Excel's _____ function is used to perform a test of independence.

CHISQ.TEST

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the _____.

Degrees of freedom

Whicch of the following hypotheses is not a valid null hypothesis? H0: µ ≥ 0 H0: µ < 0 H0: µ = 0 H0: µ ≤ 0

H0: µ < 0

A meteorologist stated that the average temperature during July in Chattanooga was 80 degrees. A sample of July temperatures over a 32-year period was taken. The correct set of hypotheses is _____.

H0: μ = 80 Ha: μ ≠ 80

The average life expectancy of tires produced by Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of its tires has increased. In order to test the validity of this belief, the correct set of hypotheses is _____.

H0: μ ≤ 40,000 Ha: μ > 40,000

Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is _____.

H0: μ ≥ 10.0% Ha: μ < 10.0%

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is _____.

H0: μ ≥ 85 Ha: μ < 85

Which of the following is an improper form of the null and alternative hypotheses? Ho: μ = μ0 and Ha: μ ≠ μ0 Ho: μ ≤ μ0 and Ha: μ > μ0 Ho: μ ≥ μ0 and Ha: μ < μ0 H0; μ < μo and Ha: μ ≥ μ0

H0; μ < μo and Ha: μ ≥ μ0

The F ratio in a completely randomized ANOVA is the ratio of _____.

MSTR/MSE

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square within treatments is _____.

SSE/(nT - k)

Which of the following is correct? SST = SSR + SSE SST = (SSR)2 SSE = SSR + SST SSR = SSE + SST

SST = SSR + SSE

The error of rejecting a true null hypothesis is _____.

Type I error

If a hypothesis test leads to the rejection of the null hypothesis, a _____.

Type I error may have been committed

The independent variable of interest in an ANOVA procedure is called _____.

a factor

An interval estimate is used to estimate _____.

a population parameter

Whenever using the t distribution in interval estimation, we must assume that _____.

a random sample was selected

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is called _____.

a residual

A Type II error is committed when _____.

a true alternative hypothesis is mistakenly rejected

A Type I error is committed when _____.

a true null hypothesis is rejected

Exhibit 10-5The following information was obtained from matched samples. Individual 1 Method 1- 7 Method 2- 5 Individual 2 Method 1- 5 Method 2- 9 Individual 3 Method 1- 6 Method 2- 8 Individual 4 Method 1- 7 Method 2- 7 Individual 5 Method 1- 5 Method 2- 6 a. Refer to Exhibit 10-5. The null hypothesis tested is H0: μd = 0. The test statistic for the mean of the population of differences is _____. b. Refer to Exhibit 10-5. If the null hypothesis is tested at the 5% level, the null hypothesis _____.

a. -1 b. should not be rejected

Exhibit 10-10The results of a recent poll on the preference of shoppers regarding two products are shown below. Product A Shoppers Surveyed- 800 Shoppers Favoring This Product- 560 Product B Shoppers Surveyed- 900 Shoppers Favoring This Product​- 612 ​ a. The point estimate for the difference between the two population proportions in favor of this product (Product A - Product B) is_____. b. At 95% confidence, the margin of error is _____. c. The 95% confidence interval estimate for the difference between the populations favoring the products is ___

a. .02 b. .044 c. -.024 to .064

Exhibit 12-6The following shows the number of individuals in a random sample of 300 adults who indicated they support the new tax proposal. Political Party Democrats- 100 Republicans- 120 Independents- 80 We are interested in determining whether the opinions of the individuals of the three groups are uniformly distributed. a. If the opinions of the individuals of the three groups are uniformly distributed, the expected frequency for each group is _____. b. The calculated value for the test statistic equals _____. c. The number of degrees of freedom associated with this problem is _____. d. The test statistic for goodness of fit has a chi-square distribution with k - 1 degrees of freedom provided that the expected frequencies for all categories are _____. e. This test for goodness of fit _____. f. The number of categories of outcomes per trial for a multinomial probability distribution is _____. g. The test for goodness of fit, test of independence, and test of multiple proportions are designed for use with ____ h. The properties of a multinomial experiment include all of the following EXCEPT _____. the experiment consists of a sequence of n identical trials three or more outcomes are possible on each trial the trials are independent the probability of each outcome can change from trial to trial

a. 100 b. 8 c. 2 d. 5 or more e. is an upper-tail test f. three or more g. categorical data h. the probability of each outcome can change from trial to trial

Exhibit 13-1 SSTR = 6,750 H0: μ1 = μ2 = μ3 = μ4 SSE = 8,000 Ha: At least one mean is different nT = 20 a. The mean square between treatments (MSTR) equals _____. b. The mean square within treatments (MSE) equals _____.​ c .The test statistic to test the null hypothesis equals _____.

a. 2,250 b. 500 c. 4.5

Exhibit 10-1Salary information regarding two independent random samples of male and female employees of a large company is shown below. Male Sample size- 64 Sample mean salary (in $1000s)- 44 Population variance-128 Female Sample size- 36 Sample mean salary (in $1000s)- 41 Population variance- 72 a. Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations (Male - Female) is _____. b. Refer to Exhibit 10-1. The standard error for the difference between the two means is _____. c. Refer to Exhibit 10-1. At 95% confidence, the margin of error is _____. d. Refer to Exhibit 10-1. The 95% confidence interval for the difference between the means of the two populations is _____. e. Refer to Exhibit 10-1. If you are interested in testing whether the average salary of males is significantly greater than that of females, the value of the test statistic is _____. f. Refer to Exhibit 10-1. The p-value is _____. g. Refer to Exhibit 10-1. At 95% confidence, we have enough evidence to conclude that the _____.

a. 3 (44-41) b. 2.0 c. 3.920 d. -.92 to 6.92 e. 1.5 f. .0668 g. null hypothesis fails to be rejected

Exhibit 10-8In order to determine whether or not there is a significant difference between the hourly wages of two companies, two independent random samples were selected and the following statistics were calculated. Company A Sample size- 80 Sample mean- $6.75 Population standard deviation- $1.00 Company B Sample size- 60 Sample mean- $6.25 Population standard deviation- $0.95 . The value of the test statistic is _____. b. The p-value is _____. c. The null hypothesis _____.

a. 3.01 b. .0026 c. should be rejected

Exhibit 12-1Individuals in a random sample of 150 were asked whether they supported capital punishment. The following information was obtained. Do You Support Capital Punishment? Yes- 40 No -60 No opinion- 50 We are interested in determining whether the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. a. .If the opinions are uniformly distributed, the expected frequency for each group would be _____. b. The calculated value for the test statistic equals _____. c. The number of degrees of freedom associated with this problem is _____. d. . The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals _____. e. What conclusion should be made?

a. 50 b. 4 c. 2 d. 5.99147 e.There is enough evidence to conclude that the distribution is uniform.

Exhibit 13-3To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment A Observations- 20, 30, 25, 33 Treatment B Observations- 22, 26, 20, 28 Treatment C Observations- 40, 30, 28, 22 a. The null hypothesis for this ANOVA problem is _____. b. The test statistic to test the null hypothesis equals _____. c. The null hypothesis is to be tested at the 1% level of significance. The critical value from the table is _____. d. The null hypothesis _____

a. μ1 = μ2 = μ3 b.1.059 c. 8.02 d. should not be rejected

In order NOT to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be _____.

at least 5

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution _____.

becomes smaller

The sampling distribution for a goodness of fit test is the _____.

chi-square distribution

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the _____.

coefficient of determination

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

completely randomized design

The probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated is the _____.

confidence coefficient

The ability of an interval estimate to contain the value of the population parameter is described by the _____.

confidence level

The confidence associated with an interval estimate is called the _____.

confidence level

A measure of the strength of the relationship between two variables is the _____.

correlation coefficient

If the coefficient of determination is a positive value, then the regression equation _____.

could have either a positive or a negative slope

As the sample size increases, the margin of error _____.

decreases

To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following EXCEPT _____. population standard deviation degrees of freedom confidence level desired margin of error

degrees of freedom

A term that means the same as the term "variable" in an ANOVA procedure is _____.

factor

An experimental design that permits statistical conclusions about two or more factors is a _____.

factorial design

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a _____.

goodness of fit test

The practice of concluding "do not reject H0" is preferred over "accept H0" when we _____.

have not controlled for the Type II error

In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____.

horizontal band of points centered near 0

In tests about a population proportion, p0 represents the _____.

hypothesized population proportion

In factorial designs, the response produced when the treatments of one factor interact with the treatments of another in influencing the response variable is known as _____.

interaction

An estimate of a population parameter that provides an interval believed to contain the value of the parameter is known as the _____.

interval estimate

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data _____.

is 1

To compute an interval estimate for the difference between the means of two populations, the t distribution _____.

is not restricted to small sample situations

The numerical value of the coefficient of determination _____.

is positive if the correlation coefficient is negative

The mean square is the sum of squares divided by _____

its corresponding degrees of freedom

SSE can never be _____.

larger than SST

Larger values of r2 imply that the observations are more closely grouped about the _____.

least squares line

When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under the curve _____.

less than or equal to the test statistic

If the cost of a Type I error is high, a smaller value should be chosen for the _____.

level of significance

For a two-tailed hypothesis test about μ, we can use any of the following approaches EXCEPT compare the _____ to the _____. value of the test statistic; critical value confidence interval estimate of μ; hypothesized value of μ p-value; value of α level of significance; confidence coefficient

level of significance; confidence coefficient

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as _____.

matched samples

The level of significance is the _____.

maximum allowable probability of a Type I error

The least squares criterion is _____.

min Σ(yi - ŷi)2

A population where each element of the population is assigned to one and only one of several classes or categories is a(n) _____.

multinomial population

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown, we must use a t distribution with _____ degrees of freedom. Let n1 be the size of sample 1 and n2 the size of sample 2.

n1 + n2 - 2

When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2, _____.

n1 and n2 can be of different sizes

Compared to the confidence interval estimate for a particular value of y (in a linear regression model), the interval estimate for an average value of y will be _____.

narrower

As the degrees of freedom increase, the t distribution approaches the _____ distribution.

normal

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is _____.

number of rows minus 1 times number of columns minus 1

Application of the least squares method results in values of the y-intercept and the slope that minimizes the sum of the squared deviations between the _____.

observed values of the dependent variable and the predicted values of the dependent variable

Regression analysis is a statistical procedure for developing a mathematical equation that describes how _____.

one dependent and one or more independent variables are related

In a goodness of fit test, Excel's CHISQ.TEST function returns a _____.

p-value

Two approaches to drawing a conclusion in a hypothesis test are _____.

p-value and critical value

When the p-value is used for hypothesis testing, the null hypothesis is rejected if _____.

p-value ≤ α

If the alternative hypothesis is that proportion of items in population 1 is larger than the proportion of items in population 2, then the null hypothesis should be _____.

p1 - p2 ≤ 0

A p-value is the _____.

probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed

The level of significance in hypothesis testing is the probability of _____.

rejecting a true null hypothesis

The number of times each experimental condition is observed in a factorial design is known as a(n) _____.

replication

The required condition for using an ANOVA procedure on data from several populations is that the _____.

sampled populations have equal variances

More evidence against Ho is indicated by _____.

smaller p-values

The standard error of x̄1 - x̄2 is the

standard deviation of the sampling distribution of x̄1 - x̄2

For the interval estimation of μ when σ is assumed known, the proper distribution to use is the _____.

standard normal distribution

Independent simple random samples are selected to test the difference between the means of two populations whose variances are not known. The sample sizes are n1 = 32 and n2 = 40. The correct distribution to use is the _____ distribution.

t

Whenever the population standard deviation is unknown, which distribution is used in developing an interval estimate for a population mean?

t distribution

An important application of the chi-square distribution is _____.

testing for goodness of fit

In hypothesis testing if the null hypothesis is rejected, _____.

the evidence supports the alternative hypothesis

In hypothesis testing, the alternative hypothesis is _____.

the hypothesis concluded to be true if the null hypothesis is rejected

In the analysis of variance procedure (ANOVA), factor refers to _____.

the independent variable

In hypothesis testing, the hypothesis tentatively assumed to be true is _____.

the null hypothesis

In a simple regression analysis (where y is a dependent and x an independent variable), if the slope is positive, then it must be true that _____.

there is a positive correlation between x and y

The ANOVA procedure is a statistical approach for determining whether the means of _____.

two or more populations are equal

A goodness of fit test is always conducted as a(n) _____.

upper-tail test

We can reduce the margin of error in an interval estimate of p by doing any of the following EXCEPT _____. increasing the sample size increasing the level of significance reducing the confidence coefficient using a planning value p* closer to .5

using a planning value p* closer to .5

As the goodness of fit for the estimated regression equation increases, the _____.

value of the coefficient of determination increases

The expression used to compute an interval estimate of μ may depend on any of the following factors EXCEPT _____. whether the population standard deviation is known the sample size whether there is sampling error whether the population has an approximately normal distribution

whether there is sampling error

In ANOVA, which of the following is NOT affected by whether or not the population means are equal?

within-samples estimate of o2

If the margin of error in an interval estimate of μ is 4.6, the interval estimate equals _____.

x̄ ± 4.6