ECON 225 FINAL

D. 94

A multiple regression analysis is conducted with 5 independent variables and an intercept on a sample of 100 observations. Suppose you want to conduct a hypothesis to test whether the coefficient of the first variable is statistically significant. What will be the degrees of freedom for this test? A. 98 B. 99 C. n − k D. 94

D. 2.40 B. Fail to reject the null hypothesis.

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized next. Sample Size Sample Mean Population St. Dev. Men 25 23 5 Women 30 28 10 At the .01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? What is the value of the test statistic for this hypothesis test? A. 2.668 B. 2.672 C. 2.58 D. 2.40 Based on your answer in question 16, what is your conclusion? A. Reject the null hypothesis and conclude the means are different. B. Fail to reject the null hypothesis. C. Fail to reject the null hypothesis and conclude the means are different. D. Reject the null hypothesis and conclude the means are the same.

B. Number of contacts

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the independent variable? A. Salesperson B. Number of contacts C. Amount of sales D. Sales manager

C. The independent variables and the dependent variable have a linear relationship

A valid multiple regression analysis assumes or requires that _________________. A. The dependent variable is measured using an ordinal, interval, or ratio scale B. The residuals follow an F distribution C. The independent variables and the dependent variable have a linear relationship D. The observations are correlated

C. sample size is important when the population is not normally distributed

According to the central limit theorem, A. the sampling distribution of the sample means is uniform B. increasing the sample size decreases the dispersion of the sampling distribution C. sample size is important when the population is not normally distributed D. the sampling distribution of the sample means will be skewed

A. The population mean.

All possible samples of size n are selected from a population and the mean of each sample is determined. What is the mean of the sample means? A. The population mean. B. It is larger than the population mean. C. It is smaller than the population mean. D. It cannot be estimated in advance.

C. 85

An analysis of the grades on the first test in ECON 225 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8. The instructor wants to award grade A to the upper 10% of the test grades. To the nearest percent, what is the dividing point between an A and a B grade? A. 80 B. 75 C. 85 D. 90

C. It approaches a normal distribution.

As the size of the sample increases, what happens to the shape of the distribution of sample means? A. It cannot be predicted in advance. B. It is positively skewed. C. It approaches a normal distribution. D. It is negatively skewed.

C. The sum of the two population variances

Assuming the population variances are known, the population variance of the difference between two means is _____________. A. The sum of the two means B. The sum of the two population standard deviations C. The sum of the two population variances D. The sum of the two ample sizes for each population

D. 0.30

Consider a multiple regression analysis involving 14 independent variables and 150 observations, with SSE = 180 and SS Total = 600. The coefficient of multiple determination is ______. A. 0.70 B. 0.40 C. 0.21 D. 0.30

C. For a 1 unit change in X3, holding X1 and X2constant, Y increases by 18 units.

Consider the following multiple regression model: Yˆ = α + 10X1 − 12X2 + 18X3. What is the interpretation of X3. A. For 18 units of change in X3, Y why changes by 1 unit. B. For a 1 unit change in X3, holding X1 and X2constant, Y decreases by 18 units. C. For a 1 unit change in X3, holding X1 and X2constant, Y increases by 18 units. D. We cannot interpret X3.

A. increase of $1 in advertising is associated with an increase of $900 in sales.

Consider the following regression analysis between sales (Y in $100) and social media advertising (X in dollars): Yˆ = 5400 + 9X. The regression equation implies that an: A. increase of $1 in advertising is associated with an increase of $900 in sales. B. increase of $1 in advertising is associated with an increase of $9 in sales. C. increase of $10 in advertising is associated with an increase of $7 in sales. D. increase of $1 in advertising is associated with an increase of $7,000 in sales.

B. The class frequency divided by the total frequency

For a relative frequency distribution, relative frequency is computed as _____________. A. The class width divided by the class interval B. The class frequency divided by the total frequency C. The class midpoint divided by the class frequency D. The class frequency divided by the class interval

D. Both are continuous distributions.

How is the t distribution similar to the standard z distribution? A. Both are discrete distributions. B. Both are skewed distributions. C. Both are families of distributions. D. Both are continuous distributions.

D. In both tails

If the alternate hypothesis states that µ /= 4,000, where is the rejection region for the hypothesis test? A. In the center B. In the upper or right tail C. In the lower or left tail D. In both tails

B. 94% of the total variation of the dependent variable is explained by the independent variable.

If the coefficient of determination (R2) is 0.94, what can we say about the relationship between two variables? A. The strength of the relationship is 0.94. B. 94% of the total variation of the dependent variable is explained by the independent variable. C. The direction of the relationship is negative. D. The direction of the relationship is positive.

A. The variables are not related.

If the correlation coefficient between two variables, X and Y, equals zero, what can be said of the variables X and Y? A. The variables are not related. B. The variables are dependent on each other. C. The variables are highly related. D. X causes Y.

F

T/F The strength of the correlation between two variables depends on the sign of the coefficient of correlation.

T

T/F. A sample statistic is a value used to estimate a population parameter.

F

T/F. Consider two populations with the same mean. Since they have the same mean then their medians must also be the same

T

T/F. If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the variances are pooled to compute the best estimated variance.

F

T/F. The 50th percentile of a distribution is the same as the distribution mean.

T

T/F. The 95% confidence interval states that 95% of the sample means of a specified sample size selected from a population will lie within plus and minus 1.96 standard deviations of the hypothesized population mean

T

T/F. The median is not affected by extremely small or extremely large values.

T

T/F. The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1.

T

T/F. The sum of deviations of each data value from the mean will always be zero.

F

T/F. When the standard deviations are equal but unknown, a test for the differences between two population means has n - 1 degrees of freedom.

B. 3/51 or 0.0588

The first card selected from a standard 52-card deck was a king. If it is NOT returned to the deck, what is the probability that a king will be drawn on the second selection? A. 1/3 or 0.33 B. 3/51 or 0.0588 C. 1/51 or 0.0196 D. 1/13 or 0.077

D. H1 : µ /= $50, 000

The mean annual incomes of certified welders are normally distributed with the mean of $50,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. Which of the following is the alternate hypothesis? A. H1 : µ = $50, 000 B. H1 : µ > $50, 000 C. H1 : µ < $50, 000 D. H1 : µ /= $50, 000

D. Marital status of college students at a particular university

The mean, as a measure of central location, would be inappropriate for which one of the following? A. Ages of adults at a senior citizen center B. Incomes of lawyers C. Number of pages in textbooks on statistics D. Marital status of college students at a particular university

D. t = +2.639

The regression equation is Yˆ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the test-statistic to test the significance of the slope? A. z = -2.560 B. z = +2.639 C. t = +2.560 D. t = +2.639

B. t = ±2.179

The regression equation is Yˆ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the critical value to test the significance of the slope at the 0.05 significance level? A. z = ±1.96 B. t = ±2.179 C. t = ±2.145 D. t = +2.145

C. σ2 is unknown

The true sampling error is usually not known because __________. A. µ is unknown B. µ is a random variable C. σ2 is unknown D. the sample mean cannot be computed

B. 25

Two samples, one of size 14 and the second of size 13, are selected to test the difference between two population means. How many degrees of freedom are used to find the critical value? Assume the population standard deviations are equal. A. 27 B. 25 C. 26 D. 14

C. n − 2

What are the degrees of freedom used to test the significance of the slope in a simple linear regression equation? A. n − 1 B. n − k C. n − 2 D. n − 1, n − 2

A. H0 : β = 0

What is the null hypothesis to test the significance of the slope in a simple regression equation? A. H0 : β = 0 B. H0 : β 6= 0 C. H0 : β ≥ 0 D. H0 : β ≤ 0

C. -1.0 to +1.0 inclusive

What is the range of values for a coefficient of correlation? A. 0 to +1.0 B. -3 to +3 inclusive C. -1.0 to +1.0 inclusive D. Unlimited range

A. The probability of success remains the same from trial to trial.

Which is true for a binomial distribution? A. The probability of success remains the same from trial to trial. B. There are ten or more possible outcomes. C. It approximates the Poisson distribution. D. It approximates the Normal distribution.

B. A probability = 0 means that the event cannot possibly occur.

Which of the following three statements about probability is true? A. Probabilities may be anywhere in the range between -1.0 and +1.0. B. A probability = 0 means that the event cannot possibly occur. C. A probability = -0.90 indicates a high probability of a negative outcome. D. None of the above statements are true.