# Problem Set

See the attached file.

You have some data on a sample of investment bankers, and are interested in the impacts of height and of seniority on their success. You estimate what you call Model A using a software package (which, like most econometrics packages, always reports p-values for two-sided hypothesis tests):

(A) SALARY = 90.2 + 26.7 HEIGHT_A + 13.9 SENIORITY - 52.3 PHD, Adj-R2 = 0.62

t=2.08 t=2.82 t=3.1

p-value=.050 p-value=.011 p-value=0.000

where

SALARY is measured in thousands of dollars, HEIGHT_A is adult height measured in inches and as deviations from average (using the male average for men, and the female average for women), SENIORITY is years with the employer, and PHD is a dummy equal to 1 if the person has a Ph.D.

a. How many observations do you have in your sample?

b. Your hypothesis about ADULT_HEIGHT is that positive deviations from average height raise a person's salary, and that negative deviations from average height lowers it. Is this a one-sided or two-sided hypothesis? ____________

c. You are not surprised that the coefficient on SENIORITY is positive. But it seems small to you, because you have recently read that "experts agree that each year of experience with an investment bank is worth another $25,000 in salary." You have a fairly small sample, so you doubt that the difference between your estimate and that of the experts is statistically significant. But you check anyway.

What is the size of the relevant standard error for your calculation? __________

What is the value of the t-statistic that you compute? ____________

What is the corresponding p-value? (If you use the table at the back of the textbook, an approximate value or a range is good enough.) ________________ ( Assume you are testing a two-sided hypothesis in this case.)

d. What salary does your model predict for a woman 70 inches tall who has been with the firm for 10 years and does not have a Ph.D.? (Assume average height for women is 65 inches)? ________

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#### Solution Preview

Please see the attached file.

You have some data on a sample of investment bankers, and are interested in the impacts of height and of seniority on their success. You estimate what you call Model A using a software package (which, like most econometrics packages, always reports p-values for two-sided hypothesis tests):

(A) SALARY = 90.2 + 26.7 HEIGHT_A + 13.9 SENIORITY - 52.3 PHD, Adj-R2 = 0.62

t=2.08 t=2.82 t=3.1

p-value=.050 p-value=.011 p-value=0.000

where

SALARY is measured in thousands of dollars, HEIGHT_A is adult height measured in inches and as deviations from ...

#### Solution Summary

What is the value of the t-statistic and other facets in this post?

Hypothesis Testing Multiple Choice Problem Set

I am having some trouble with a few problems. Any help is appreciated

A grocery store owner is interested in determining if the average weight of a package of ground beef sold in the store weighs one pound. An appropriate null hypothesis for this study is

a. H0: m = 1 lb

b. H0: m ¹ 1 lb

c. H0: m > 1 lb

d. H0: m < 1 lb

The rejection region for a two-tail test that uses the standard normal distribution is that area under the distribution lying

a. between 0 and the positive cutoff value for Z.

b. between the positive cutoff value for Z and the negative cutoff value for Z.

c. between 0 and the negative cutoff value for Z.

d. to the right of the positive cutoff value for Z and to the left of the negative cutoff

value for Z.

A restaurant manager thinks that the average bill paid by his customers is $25. To test his hypothesis, the next 50 tabs are tallied. All of them are over $25. Therefore, he can conclude immediately that the average bill paid by all of his customers

a. exceeds $25.

b. equals $25.

c. is less than $25.

d. may be less than, equal to, or greater than $25.

The appropriate alternative hypothesis for a two-tail test to determine if mean body weight of all the men who have joined a health club is 185 pounds would be

a. HA: m = 185 lb.

b. HA: m < 185 lb.

c. HA: m > 185 lb.

d. HA: m ¹ 185 lb.

The appropriate null hypothesis for an upper-tail test to determine if mean body weight of all the men who have joined a health club exceeds 185 pounds would be

a. HA: m = 185 lb.

b. HA: m > 185 lb.

c. HA: m £ 185 lb.

d. HA: m ¹ 185 lb.

Two samples of shelled corn were taken from a bin and the weight of each kernel was measured and compared to the mean from last year's entire bin. The test statistic from the first sample was 1.8, the test statistic from the second sample was 2.5, and the research team was astonished to learn that the mean and standard deviation were identical for both samples. If the first sample was composed of 16 kernels, how many kernels were weighed on the second occasion?

a. 8

b. 12

c. 22

d. 31

A sample of 22 observations is collected in order to perform a chi-square test of a single variance. If the hypothesized variance of the population equals the variance of the sample, what is the value of the chi-square test statistic?

a. 21

b. 22

c. 23

d. 43

A chi-square test statistic was calculated to be 18, based on a sample variance of 20 and a hypothesized population variance of 40. How many observations were made when the sample was extracted?

a. 9

b. 10

c. 36

d. 37

A researcher has decided to conduct a lower-tail test for a hypothesized population variance of 24. What is the appropriate null hypothesis for the study?

a. H0: s2 £ 24

b. H0: s2 ³ 24

c. H0: s2 ³ 24

d. H0: s2 < 24

The same sample can be used to identify two populations for comparison provided that the variable being used to define the population is

a. qualitative.

b. quantitative.

c. continuous.

d. ordinal.

What must be checked in order to compare two population means when you do not know the values of the population standard deviations?

a. the range

b. the standard deviation of each sample

c. the distribution of the test statistic

d. the size of the sample

A large sample Z test for the difference between two population means does not require that the two populations be _________ distributed, but the t test applied to small samples requires that the two populations be _________ distributed.

a. normally, binomially

b. binomially, normally

c. normally, normally

d. binomially, binomially

Which of the following examples illustrates a study that compares two population proportions?

a. The amount of saliva secreted daily by men and women.

b. The volume of air breathed daily by track runners and swimmers.

c. The percentage of men and women who are color blind.

d. The pounds of food digested daily by adult crocodiles and water buffaloes.

When comparing sample variances, the best way to compare them is to

a. divide one by the other.

b. add them together.

c. subtract one from the other.

d. multiply them together.

The test statistics for the ratio of two sample variances is the ____________ statistic.

a. Z

b. F

c. t

d. chi-square

The shape of the F distribution is

a. symmetric.

b. skewed right.

c. skewed left.

d. the same as the t distribution.

A(n) _____________ is a variable that can be used to differentiate one group or population from another.

a. factor

b. level

c. observation

d. replicate

A bar soap manufacturer is conducting an experiment to determine how people react to 3 different brand names. Each brand name represents a(n) ___________ of the experimental factor.

a. replicate

b. observation

c. level

d. variable

The technique that is used to determine if more than two population means are equal by analyzing the variation in the data is known as

a. chi-square.

b. analysis of variance.

c. correlation analysis.

d. least squares regression.

The mean of all the observations of an experiment is called the ___________ mean.

a. group

b. treatment

c. block

d. grand

Each observation of a one-way experiment can be divided into component parts. What is the correct relationship between them?

a. Grand mean = Response + Treatment effect + Error

b. Treatment Effect = Response + Grand mean + Error

c. Error = Grand mean + Treatment effect + Response

d. Response = Grand mean + Treatment effect + Error

The chi-square test compares the __________ frequency distribution of the data to the frequency distribution that would be __________ if the null hypothesis were __________.

a. observed, expected, true

b. observed, expected, false

c. expected, observed, true

d. expected, observed, false

A distribution in which each outcome of a class of outcomes is equally likely to occur is called a ___________ distribution.

a. binomial

b. normal

c. chi-square

d. uniform

The distribution of single digits extracted sequentially from a table of random numbers would most likely resemble a ___________ distribution.

a. binomial

b. normal

c. chi-square

d. uniform

Which one of the following distributions of counts data would most likely be uniform?

a. letters of the alphabet from the front page of a newspaper

b. vehicles with their headlights on at different hours of the day

c. odd and even numbers drawn in the daily state lottery

d. meteors visible to the naked eye at different hours during a meteor shower

The following table summarizes the number of observations in each of three classes.

Class Observed Frequency

1

2

3 40

60

100

If the chi-square test statistic equals zero, what were the expected probabilities in the null hypothesis?

a. p1 = 0.4, p2 = 0.2, p3 = 0.4

b. p1 = 0.2, p2 = 0.3, p3 = 0.5

c. p1 = 0.3, p2 = 0.2, p3 = 0.5

d. p1 = p2 = p3 = 1/3

The least squares method finds the equation of the line that __________ the __________ of the squared deviations between the points and the line.

a. maximizes, sum

b. minimizes, product

c. minimizes, sum

d. maximizes, product

A linear regression between Y and X produced the following equation for the least squares line:

[img src="@4435602"]= 2.15 - 3.2x

Which of the following statements concerning this relationship is true?

a. For every one-unit increase in X, Y increases 3.2 units.

b. For every one-unit increase in Y, X decreases 3.2 units.

c. For every one-unit increase in X, Y decreases 3.2 units.

d. For every one-unit increase in Y, X increases 3.2 units.

A least squares line for variables X and Y has been found in which the value of the slope is 3 and the intercept is 2. At this point we can conclude that

a. variable X causes variable Y to occur.

b. there is a positive relationship between variables X and Y.

c. there may be a relationship between variables X and Y.

d. there is no relationship between variables X and Y.

A regression line has been found that has nearly all the points lying directly on the line, and only a few of them stray away from the line. Therefore, the standard error of the estimate is likely to be

a. huge.

b. small.

c. 0.

d. undefined.

A regression line for two variables has been found with a slope coefficient of 2.35 and an intercept of 1. If the standard error of the coefficient is 0.2, what can be concluded?

a. The linear relationship is insignificant.

b. The regression line is almost horizontal.

c. The regression line is almost vertical.

d. There is a significant linear relationship between the two variables.

An airline is concerned that its flights will be overbooked during a popular holiday, sending the load factor "through the roof." A regression model has been constructed to estimate load factors throughout the year. What should be used to estimate the holiday load factor?

a. a prediction interval

b. a confidence interval

c. the residual value

d. the mean load factor

A -0.947 correlation coefficient has been found between two variables after examining 43 pairs of observations. What can be concluded?

a. There is a strong positive relationship between the two variables.

b. There is a strong negative relationship between the two variables.

c. There is a weak positive relationship between the two variables.

d. There is a weak negative relationship between the two variables.

There are basic assumptions surrounding the error term in the least squares regression model. All of the following are assumptions except

a. the mean value is 0.

b. it is normally distributed.

c. the standard deviation is 1.

d. different observations produce uncorrelated error terms.

A regression model has been constructed in which the residuals are known to be normally distributed. A normal probability plot would yield a pattern that resembles

a. a straight line.

b. the normal distribution.

c. a random scatter.

d. a curve, either concave upward or downward.

A set of time series data is showing no particular upward or downward trend. All of the following techniques would be appropriate to use except

a. exponential smoothing.

b. regression.

c. simple moving average.

d. weighted moving average.

Time series models are used to ___________ past behavior in order to predict future behavior.

a. extrapolate

b. interpolate

c. project

d. simulate

Horace Mann, principal of Jones Public School, has decided to construct a time series model to obtain a 2- and a 3-period moving average to forecast student enrollments for next term. Which statement is true concerning the accuracy of each forecast that Horace will obtain?

a. The 2-period forecast will be more accurate than the 3-period forecast.

b. The 3-period forecast will be more accurate than the 2-period forecast.

c. Both forecasts will be equally accurate.

d. Either forecast could be more accurate than the other.

Jimmy Jackson is using time series data to obtain an inventory forecast. There are 15 periods in all, the three most recent periods are being used for the forecast, and the weights that are being applied to all three periods are unequal. What technique is Jimmy using to obtain the forecast?

a. simple moving average

b. weighted moving average

c. exponential smoothing

d. regression

A regression model can be applied to time series data in order to obtain a forecast provided the dependent variable shows

a. either an upward or a downward trend.

b. an upward trend but not a downward trend.

c. a downward trend but not an upward trend.

d. neither an upward nor a downward trend.

Jerry Slater is applying a simple regression model to time series data. Jerry can calculate the mean square error (MSE) by averaging the sum of the

a. predicted values of the dependent variable.

b. actual values of the dependent variable.

c. residuals.

d. squares of the residuals.