QBA 2305 Final Burrow

Which one of the following is not an assumption of one-way analysis of variance?

**equality of the population means** equality of the population VARIANCES random selection of samples from each population Samples selected from each treatment population all have normal distributions.

In a simple linear regression model, the intercept term is the mean value of y when x equals ________.

0

Assume that the following data set is not normally distributed. (21, 18, 4, 9, 14, 16, 17, 12, 15, 8, 7, 5) If Ha: Md < 6, then the value of S is

2. S is the number of sample measurements less than 6, so S = 2

The number of degrees of freedom associated with a chi-square test for independence based upon a contingency table with 4 rows and 3 columns is ________.

6 df = (4 − 1)(3 − 1) = 6

A manufacturer of cell phone batteries claims that the median life of a battery is more than 40 hours. Suppose a random sample of 75 batteries finds that 32 have a life of more than 40 hours. Using α = .05, can we conclude that the battery life is more than 40 hours?

Do not reject the null hypothesis; z = −1.38. The test failed to reject H0, so we can't conclude that the battery life is more than 40 hours.

In multiple regression analysis, the mean square regression divided by mean square error yields the ________.

F statistic

Testing the contribution of individual independent variables with t tests is performed prior to the F test for the model in multiple regression analysis.

False: An Ftest is performed first to determine whether there is a reason to do individual t tests.

A significant positive correlation between X and Y implies that changes in X cause Y to change.

False: Correlation does not assume or imply causation.

When using simple regression analysis, if there is a strong correlation between the independent and dependent variables, then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.

False: Correlation does not assume or predict causation or direction.

Expected cell frequencies for a multinomial distribution are calculated by assuming statistical dependence.

False: Expected cell frequencies are calculated by assuming statistical independence.

The experimental region is the range of the previously observed values of the dependent variable.

False: Experimental region is the range of values of the independent variable.

In one-way ANOVA, a large value of F results when the within-treatment variability is large compared to the between-treatment variability.

False: F is the MST/MSE, so F is large with a larger between-treatment variability.

When we carry out a chi-square test of independence, in the alternative hypothesis we state that the two classifications are statistically independent.

False: In the chi-square test of independence, the null hypothesis is that the two classifications are independent.

The Wilcoxon rank sum test requires that two independent samples being compared must have equal sample sizes.

False: No sample size assumptions are necessary for a Wilcoxon rank sum test

A sign test is a test of hypothesis about the population mean.

False: Sign test uses population median.

The Wilcoxon rank sum test is a nonparametric test used to compare the central tendencies of two populations when a paired difference experiment has been conducted.

False: The Wilcoxon signed ranks test is used when a paired difference experiment has been conducted.

The multiple correlation coefficient can assume any value between zero and 1, inclusive.

False: The multiple correlation coefficient has values between −1 and +1.

The sign test is a nonparametric test for a population mean that is valid for any sample size and population shape.

False: The sign test is conducted on a population median.

The error sum of squares measures the between-treatment variability.

False: The treatment sum of squares measures the between-treatment variability.

The variance inflation factor measures the relationship between the dependent variable and the rest of the independent variables in the regression model.

False: VIF measures multicollinearity (when independent variables are related to each other).

The EPA has stipulated that the Pollution Standard Index (PSI) for clean air standards is to average no more than 100. A random sample of 9 days for the city of Acme showed PSI readings of 144, 85, 90, 120, 150, 105, 93, 130, and 115. The EPA wants to test to determine if Acme air is dirtier than the stipulated clean air standards. Assume the population of PSI readings is highly nonnormal and state the null hypothesis.

H0: Md ≤ 100 H0: Md ≤ 100, HA: Md > 100

The point estimate of the variance in a regression model is

MSE

In one-way ANOVA, the total sum of squares is equal to ________.

Treatment SS + Error SS

A one-way analysis of variance is a method that allows us to estimate and compare the effects of several treatments on a response variable.

True

A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and an independent variable.

True

If r = −1, then we can conclude that there is a perfect relationship between X and Y.

True

In a completely randomized (one-way) ANOVA, with other things being equal, as the sample means get closer to each other, the probability of rejecting the null hypothesis decreases.

True

In a contingency table, when all the expected frequencies equal the observed frequencies, the calculated χ2 statistic equals zero.

True

In a multiple regression analysis, if the normal probability plot exhibits approximately a straight line, then it can be concluded that the assumption of normality is not violated.

True

In one-way ANOVA, other factors being equal, the further apart the treatment means are from each other, the more likely we are to reject the null hypothesis associated with the ANOVA F test.

True

In performing a chi-square goodness-of-fit test with multinomial probabilities, the smaller the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct.

True

Parametric tests, such as F and t tests, are more powerful than their nonparametric counterparts if the assumptions needed to perform the parametric test are not violated.

True

Regression models that employ more than one independent variable are referred to as multiple regression models.

True

When using the chi-square goodness-of-fit test, if the value of the chi-square statistic is large enough, we reject the null hypothesis.

True

A copy machine service company provides maintenance and repair service for different types and brands of copiers. The manager of the repair department wants to know if the repair time for brand A is higher than the repair time for brand B. The manager randomly selects 8 repair records associated with brand A and 8 repair records associated with brand B. The distribution of repair times for both brand A and brand B is highly skewed. Which one of the following nonparametric tests is appropriate for this problem?

Wilcoxon rank sum test The rank sum test is used when comparing two independent populations with small sizes and not normally distributed.

The chi-square goodness-of-fit is ________ a one-tailed test with the rejection region in the right tail.

always

The ________ units are the entities (objects, people, etc.) to which the treatments are assigned.

experimental

As the difference between observed frequency and expected frequency ________, the probability of rejecting the null hypothesis increases.

increases

When we carry out a chi-square test of independence, as the differences between the respective observed and expected frequencies decrease, the probability of concluding that the row variable is independent of the column variable

increases. When a chi-square test for independence is large (observed frequencies differ substantially from the expected frequencies), then doubt will be cast on the null hypothesis of independence. Therefore, a small difference will result in a small chi-square and lowers the likelihood of rejecting the null hypothesis of independence.

The effects of different levels of qualitative independent variables are described using ________ variables.

indicator

In a multiple regression analysis, if the normal probability plot ________, then it can be concluded that the assumption of normality is not violated.

is a straight line

An investigator hired by a client suing for sex discrimination has developed a multiple regression model for employee salaries for the company in question. In this multiple regression model, the salaries are in thousands of dollars. For example, a data entry of 35 for the dependent variable indicates a salary of $35,000. The indicator (dummy) variable for gender is coded as X1 = 0 if male and X1 = 1 if female. The computer output of this multiple regression model shows that the coefficient for this variable (X1) is −4.2. The t test showed that X1 was significant at α = 0.1. This result implies that for male and female workers of the company,

on the average, females earn $4,200 less.

The dependent variable, the variable of interest in an experiment, is also called the ________ variable.

response

Five years ago, the average starting salary of a new college graduate with a major in marketing was $34,000. A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 38, 36, 25, 37, 35, 24, 38, 45, 39, 36. The local university wants to determine if the starting salaries have increased in the last five years. Assume that the population of starting salaries in marketing is not normally distributed. Which one of the following tests is appropriate for this problem?

sign test With a small sample and highly skewed sample population, the sign test is the appropriate test to use.

In simple regression analysis, the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the

slope of the regression line.

In a one way ANOVA table, the ________ the value of MSE, the higher the probability of rejecting the hypothesis that all treatment means are equal.

smaller

The least squares regression line minimizes the sum of the

squared differences between actual and predicted Y values.

The ________ distribution is used for testing the significance of the slope term.

t

In multiple regression analysis, which one of the following is the appropriate notation for error (residual)?

yi - y(hat)i