CISB Exam 2

One of the major automobile makers has developed two new engines. At question is whether the two engines have the same variability with respect to miles per gallon. The appropriate null and alternative hypothesis are: Ho: σ12 ≠ σ22 Ha: σ12 = σ22

False

If the coefficient of determination is .45, this can be interpreted as 45% of the variation in the y-variable can be explained by knowing the x-variable.

True

In conducing one-way analysis of variance, the population distributions are assumed normally distributed.

True

Managers use contingency analysis to determine whether two categorical variables are independent of each other.

True

Of the two types of statistical errors, the one that decision makers have most control over is Type I error (the value of alpha).

True

Recently, a company tested three different machine types to see if there was a difference in the mean thickness of products produced by the three. A random sample of ten products was selected from the output from each machine. Given this information, the proper design to test whether the means are equal is a one-way ANOVA balanced design.

True

The F-distribution can only have positive values.

True

The coefficient of determination (R Square) is always found by taking the correlation coefficient (r) and squaring it.

True

The following regression model has been computed based on a sample of twenty observations: y = 34.2 + 19.3x Given this model, the predictive model for y when x=40 is 806.2.

True

The proportions in the joint frequency table can be used to find relative probability for a specified category.

True

The test statistic for the mean is the value calculated from the sample using =(xbar-µ)/(stdev/sqrt(n).

True

To employ contingency analysis, we set up a 2-dimensional table with rows and columns called a contingency table, which can also be referred to as a cross-tabulation or a joint frequency table.

True

Two samples are independent when the occurrence of values in one sample has no influence on the probability of the occurrence of values in the second sample.

True

In conducting a test of independence for a contingency table that has 4 rows and 3 columns, the number of degrees of freedom is 11.

False

Order the steps of a hypothesis test (1-5):

3. Calculate the value from the sample i.e., use the sample information to calulate the sample z or t or p 2. How are we measuring it? What is the critical value for the test? Reject Ho if ________ i.e., z-value or t-value (from the charts) or p-value 5. Business Conclusion: What does this mean in relation to the business? How could you use the information? 1. What are we trying to test/show? Formulate the null and alternative hypothesis: Ho: _______ Ha: _______ 4. Statistical Conclusion: Reject Ho, based on the sample there is enough evidence to show <insert text from Ha> or Do not reject Ho, based on the sample there is not enough evidence to show <insert text from Ha>

In a contingency analysis, the greater the difference between the actual and the expected frequencies, the larger the chi-square value and the more likely:

A) H0 should be rejected.

If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000. The best null and alternative hypothesis is: Question options: A) Ho: µ > 25,000 Ha: µ ≤ 25,000 B) Ho: µ = 25,000 Ha: µ ≠ 25,000. C) Ho: µ ≤ 25,000 Ha: µ > 25,000 D) Ho: xbar ≤ 25,000 Ha: xbar > 25,000

C) Ho: µ ≤ 25,000 Ha: µ > 25,000

There have been complaints recently from homeowners in the north end claiming that their homes have been assessed at values that are too high compared with other parts of town. They say that the mean increase from last year to this year has been higher in their part of town than elsewhere. To test this, the assessor's office staff plans to select a random sample of north end properties (group 1) and a random sample of properties from other areas within the city (group 2) and perform a hypothesis test. Based on the information provided, the research (or alternate) hypothesis is: Question options: A) Ha: µ1 > µ2 B) Ha: µ1 ≠ µ2 C) Ha: µ1 = µ2 D) Ha: µ1 < µ2

A) Ha: µ1 > µ2

A hotel chain has four hotels in Oregon. The general manager is interested in determining whether the mean length of stay is the same or different for the four hotels. She selects a random sample of n = 20 guests at each hotel and determines the number of nights they stayed. Assuming that she plans to test this using an alpha level equal to 0.05, which of the following is the appropriate alternative hypothesis? Question options: A) Not all population means are equal. B) Ho: μ1 = μ2 = μ3 = μ4 C) Ho: μ1 ≠ μ2 ≠ μ3 ≠ μ4 D) σ1 = σ2 = σ3 = σ4

A) Not all population means are equal.

A study comparing package weight (x) to the cost of shipping (y). The Excel Data Analysis Regression output is as follows: Given this, we can say: Question options: A) Approximately 91 percent of the variation in shipping cost (y) can be explained by knowing the package weight (x). B) Approximately 82 percent of the variation in shipping cost (y) can be explained by knowing the package weight (x). C) Approximately 82 percent of the variation in package weight (y) can be explained by knowing the shipping cost (x). D) Approximately 91 percent of the variation in package weight (y) can be explained by knowing the shipping cost (x).

B) Approximately 82 percent of the variation in shipping cost (y) can be explained by knowing the package weight (x).

In conducting a one-way analysis of variance where the critical value = 41.2 and the test statistic = 31.6, which of the following is correct? Question options: A) Conclude that the means are not all the same and that that the Tukey-Kramer procedure is not needed B) Conclude that all means are the same and there is no need to conduct the Tukey-Kramer procedure C) Conclude that the means are not all the same and that that the Tukey-Kramer procedure should be conducted D) Conclude that all means are the same and that the Tukey-Kramer procedure should be conducted

B) Conclude that all means are the same and there is no need to conduct the Tukey-Kramer procedure

It is believed the SAT scores for students entering two universities may have different standard deviations. Specifically, it is believed the standard deviation at University A is greater than the standard deviation at University B. If a statistical test is to be conducted, which of the following would be the proper way to formulate the alternative hypothesis? Question options: A) Ha: σA < σB B) Ha: σA2 > σB2 C) Ha: σA2 - σB2 ≠ 0 D) Ha: σA2 < σB2

B) Ha: σA2 > σB2

Which of the following is the appropriate null hypothesis when testing whether two population variances are equal? A) Ho: σ2/1 > σ2/2Ho: σ1/2 > σ2/2 B) Ho: σ2/1 ≥ σ2/2Ho: σ1/2 ≥ σ2/2 C) Ho: σ2/1 = σ2/2Ho: σ1/2 = σ22 D) Ho: σ2/1 ≠ σ2/2Ho: σ1/2 ≠ σ22

C) Ho: σ2/1 = σ2/2

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, which of the following would be the correct formulation of the null and alternative hypotheses? Question options: A) Ho: xbar = 16 Ha: xbar ≠ 16 B) Ho: µ = 16 Ha: µ ≠ 16 C) Ho: µ ≤ 16 Ha: µ > 16 D) Ho: µ ≥ 16 Ha: µ < 16

B) Ho: µ = 16 Ha: µ ≠ 16

To use contingency analysis for numerical data, which of the following is true? Question options: A) Contingency analysis cannot be used for numerical data. B) Numerical data should be grouped into numeric ranges to get them into categories. C) Contingency analysis can be used for numerical data only if both variables are numerical. D) Contingency analysis can be used for numerical data only if it is interval data.

B) Numerical data should be grouped into numeric ranges to get them into categories.

Which distribution is used in testing the hypotheses about the equality of two population variances? A) Χ2 distribution B) t-distribution C) F-distribution D) z-distribution

C) F-distribution

When testing a two-tailed hypothesis using a significance level of 0.05, a sample size of n = 16, and s=5.2, which of the following is true? Question options: A) A sample size of 16 is not large enough to run a hypothesis test. B) All options are correct. C) The alpha probability must be split in half with 2.5% in the lower tail and 2.5% in the upper tail. D) The test statistic will be a z-value.

C) The alpha probability must be split in half with 2.5% in the lower tail and 2.5% in the upper tail.

A conclusion to "not reject" the null hypothesis is the same as the decision to "accept" the null hypothesis.

False

The managers for a vegetable canning facility claim the standard deviation for the ounces per can on the new automated line is less than for the older manual line. Given this, the correct null and alternative hypotheses for performing the statistical test are: Ho: σ1 = σ2 Ha: σ1 ≠ σ2

False

The police chief in a local city claims that the average speed for cars and trucks on a stretch of road near a school is at least 45 mph. If this claim is to be tested, the null and alternative hypotheses are: Ho: µ < 45 Ha: µ ≥ 45

False

A two-tailed test for two population variances could have a null hypothesis like the following: Ho:σ 2/1 = σ 2/2 Ho:σ 1/2 = σ 2/2

True

An expected cell value of 5 or more is important to ensure an error is not made in the decision making process.

True

Box-and-whisker plots are often useful for determining whether one or more populations might be normally distributed.

True

Contingency analysis helps to make decisions when multiple proportions are involved.

True

A correlation coefficient (r) is computed from a sample and is subject to sampling error. The hypothesis test to see if there the correlation coeffiecent is 0 (meaning no correlation) would use the greek r which is represented as ρρ

True

A critical value for a hypothesis test on a mean could be the z or t value that is associated with the acceptable percent of error (alpha) in the tail(s) of the curve. These can be found using either =norm.s.inv(%) or t.inv(%,n-1).

True

A recent study of students at the university contained data on year in school and student age. An appropriate tool for analyzing the relationship between these two variables would be a joint frequency distribution followed by a contingency analysis.

True

The t-distribution is used to test whether two sample variances are equal.

False

The test statistic that is used when testing a null hypothesis for a population variance is the standard normal z-value.

False

A potato chip manufacturer has found that in the past the standard deviation of bag weight has been 0.2 ounces. They want to test whether the standard deviation has changed. The null hypothesis is: Question options: Ho: σ2 = 0.2 Ho: σ = 0.2 Ho: σ = 0.04 Ho: σ2 = 0.04

Ho: σ2 = 0.04

A two-tailed hypothesis test with alpha = 0.05 is similar to a 95 percent confidence interval.

True

For a given significance level, increasing the sample size will tend to increase the chi-square critical value used in testing the null hypothesis about a population variance.

True

Hypothesis testing is about proving something beyond a reasonable doubt.

True

In Excel a joint frequency distribution table can be created using a tool called PivotTable.

True

In a contingency analysis the expected values are based on the assumption that the two variables are independent of each other.

True

The one-way ANOVA test involves assuming that the population variances are equal.

True

The pooled variance mathematically combines the variances of the two populations and combines it into a single value.

True

The results of a regression analysis indicate: WeeklySales$(y) = $1242 + $2.32 * Ad$Spent(x) Is it true that the equation tells us that for every $1 increase in Ad$Spent, the WeeklySales$ increases by $2.32?

True

When constructing a scatter plot, the dependent variable (what we are trying to predict) is placed on the vertical y-axis and the independent variable is placed on the horizontal x-axis.

True

When the slope in the regression equation is negative, the correlation coefficient (r) will always be negative.

True

When using a chi-square test for the variance of one population, we are assuming that the population is normally distributed.

True

The cost of a college education has increased at a much faster rate than costs in general over the past twenty years. In order to compensate for this, many students work part- or full-time in addition to attending classes. At one university, it is believed that the average hours students work per week exceeds 20. To test this at a significance level of 0.05, a random sample of n = 20 students was selected and their weekly work hours recorded. Given we are trying to prove the hours are more than 20, this goes into Ha as follows: Ho: μ ≤ 20 hours Ha: μ > 20 hours Which of the following is a correct rejection statement? Question options: A) Reject Ho if t > 1.729 B) Reject Ho if t < -1.729 C) Reject Ho if z > 1.645 D) Reject Ho if z < -1.645

A) Reject Ho if t > 1.729

The following is Excel Data Analysis output for Regression. The data is comparing the customer satisfaction rating (y) based on the drive thru service time in minutes (x): Which of the following is true? Question options: A) The correlation coefficient (r) is -0.8851. B) The correlation coefficient (r) is 0.7835. C) The correlation coefficient (r) is 0.8851. D) The correlation coefficient (r) is -0.7835.

A) The correlation coefficient (r) is -0.8851.

If the population correlation between two variables is determined to be -0.70, which of the following is known to be true? Question options: A) There is a fairly strong negative linear relationship between the two variables. B) There is a positive linear relationship between the two variables. C) An increase in one of the variables will cause the other variable to decline by 70 percent. D) The scatter diagram for the two variables will be upward sloping from left to right.

A) There is a fairly strong negative linear relationship between the two variables.

A regression analysis between sales (Y) and advertising (X) (both in dollars) resulted in the following equation: y = 100+200x The above equation implies that an Question options: A) increase of $10 in advertising is correlated with an increase of $2,000 in sales. B) increase of $10 in advertising is correlated with an increase of $2100 in sales. C) increase of $10 in advertising is correlated with an increase of $100 in sales. D) increase of $10 in advertising is correlated with an increase of $20 in sales.

A) increase of $10 in advertising is correlated with an increase of $2,000 in sales.

When using the Tukey Kramer procedure, you will need to find the q-value using Appendix I in your textbook. Assume we just finished a test to see if the average time it took 4 employees to finish a task was equal. After a sample of 5 observations from each employee, the results showed that at least one mean was different. If α = .05α = .05 Hint: There are four categories (k=4 for the column) and the d.f for a sample of 20 with four categories (d.f. = n - k = 20-4 = 16 for the row). There are two charts in Appendix I, one is 95% and one is 99%. If α = .05α = .05

A) q = 4.05

In order for a one-way analysis of variance to be considered a balanced design, which of the following must hold? Question options: A) The population variances must be equal. B) The sample sizes selected from each population must be equal. C) The study must have the same number of rows as it does columns. D) All of the above are true.

B) The sample sizes selected from each population must be equal.

When writing the null and alternative hypothesis, which of the following is not true: Question options: A) When testing for a mean, Ho and Ha is testing μ. Example, Ho: μ =12. B) When testing for a mean, Ho and Ha is testing xbar. Example, Ho: xbar = 12. C) Ho will always have an equality such as =, ≤, or ≥ D) Ha should have the opposite sign of Ho, such as ≠, >, or <.

B) When testing for a mean, Ho and Ha is testing xbar. Example, Ho: xbar = 12.

Given the result of a contingency analysis is to reject Ho and the two categories are found to be dependent: Question options: A) This means the chi-square was larger enough to be in the upper tail. B) To find a potential pattern, you could review the cells where there is the largest difference between the observed and expected values that also have high chi-square values. C) Further study and testing will be needed to conducted to prove what the relationships might be. D) All options are true.

D) All options are true.

A recent study posed the question about whether Japanese managers are more motivated than American managers. A randomly selected independent sampling method was administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample Size 211 100 Mean SSATL Score65.75 79.83 Sample Std. Dev. 11.07 6.41 A test on the variances was done first and concluded the the standard deviation between the two samples are not equal. Looking at the formula sheet, which test would be most appropriate? A) F-test B) t-test, assuming unequal variances, where d.f. =complex formula C) z-test, assuming unequal variances D) t-test, assuming equal variances, where d.f. = n1 + n2 -2, and you must compute a pooled standard deviation (sp)

B) t-test, assuming unequal variances, where d.f. =complex formula

A hypothesis test for the difference between two means is considered a two-tailed test when: Question options: A) the standard deviations are unknown. B) the null hypothesis states that the population means are equal. C) the population variances are equal. D) the alpha level is 0.10 or higher.

B) the null hypothesis states that the population means are equal.

The first phase of a hypothesis test is to determine what we are testing. Which of the following is not mentioned as a type of hypothesis test? A) A status quo test to see if operations are running normally or if a situation has changed. B) A similarity test that proves a value is equal to a desired value. C) A research hypothesis to prove a product is superior than an existing product. D) A test in order to prove a claim.

B) A similarity test that proves a value is equal to a desired value.

Joint frequency distributions are used to display: Question options:A) the histograms of two variables analyzed simultaneously.B) the number of occurrences at each of the possible joint occurrences of two variables.C) the cumulative distribution of a variable with two possible outcomes.D) the relative frequency of two variables.

B) the number of occurrences at each of the possible joint occurrences of two variables.

When testing/estimating the difference between two means using the method where sample variances are pooled, which of the following assumptions is not needed? Question options: A) The samples are independent. B) The populations have equal variance. C) The sample sizes are equal. D) The populations are normally distributed.

B,C

A commuter has two different routes available to drive to work. She wants to test whether route A is faster than route B. The best hypotheses are: Question options: A) Ho: µA ≥ µB Ha: µA < µB B) Ho: µA < µB Ha: µA ≥ µB C) Ho: µA = µB Ha: µA ≠ µB D) Ho: µA ≤ µB Ha: µA > µB

C) Ho: µA = µB Ha: µA ≠ µB

A regression test was conducted to help in predicting the price of milk in Colorado (y) based on the gasoline prices in Florida (x). The results showed that there was a strong correlation (r=.85). In looking at the analysis a statistician said the results indicated a spurious correlation. What did the statistician mean by a spurious correlation? Question options: A) The correlation is valid and you can use the cost of gas in Florida to predict the cost of milk in Colorado. B) The test contained mathematical errors. C) The correlation is invalid because it is between two seemingly unrelated variables. D) None of the above.

C) The correlation is invalid because it is between two seemingly unrelated variables.

How can the degrees of freedom be found in a contingency table with cross-classified data?

C) The df are equal to (number of rows minus 1) multiplied by (number of columns minus 1)

For a chi-square test involving a contingency table, suppose H0 is rejected. We conclude that the two variables are: Question options:A) curvilinear.B) linear.C) related.D) not related.

C) related.

A cell phone company wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers. To conduct a contingency analysis, the number of degrees of freedom is: A) 6. B) 5. C) 3. D) 2.

D) 2.

Under what conditions can the t-distribution be correctly employed to test the difference between two population means? Question options: A) When the population variances are unknown B) When the two populations of interest are assumed to be normally distributed C) When the population variances are assumed to be equal D) All of the options are required.

D) All of the options are required.

A study was done to see if the cost of the meal (x) could be used to predict the amount tipped (y). A random sample of bills and resulting tips were collected. The smallest bill was $9 and the largest bill was $89 in the sample. The following regression results were observed: Given this output, which of the following is true? Question options: A) The point estimate for the slope is 0.192. B) We are 95% confident that the true slope is between .158 and .226. C) y = -1.2362 + .1921 * x for values of x between $9 and $89. D) All of the options are true.

D) All of the options are true.

Let's say we conduct a hypothesis test on the regression slope coefficient (r): Ho: ρ=0 (no correlation)Ha: ρ≠0 (is a correlation)Ho: ρ=0 (no correlation)Ha: ρ≠0 (is a correlation) We find that the t-value and p-value are not in the tail and we do not reject Ho. This means: Question options: A) there is not enough evidence to show there is a linear correlation. With the given the sample size, r is not close enough to 1 or -1 to say there is a linear correlation. B) since we can't prove there is a correlation, there is not a predictive equation. We should ignore the output for intercept and slope and consider it invalid for an equation. C) when you view the the scatter plot, it is either a curvilinear pattern or there is no pattern. D) All of the options are true.

D) All of the options are true.

In developing a scatter plot, it is proper to draw lines between all the points.

False

If a hypothesis test for a single population variance is to be conducted, which of the following statements is true? Question options: A) The null hypothesis must be stated in terms of the population variance. B) The chi-square distribution is used. C) If the sample size is increased, the critical value is also increased for a given level of statistical significance. D) All options are true.

D) All options are true.

When the the observed value of one or more cells is less than 5, which of the following is true? Question options: A) You could increase the overall sample size. B) You could try to combine categories when some categories have some natural fit together. C) If Ho is not rejected (there was not enough difference between the expected and observed values), then there is no issue with a Type I error and no need for further action. D) All options are true.

D) All options are true.

A recent study posed the question about whether Japanese are managers more motivated than American managers. A randomly selected sample of each was administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample Size. 211 100 Mean SSATL Score65.75 79.83 Population Std. Dev.11.07 6.41 Which of the following is the correct the null and alternative hypotheses to determine if the average SSATL score of Japanese managers differs from the average SSATL score of American managers? Question options: A) Ho: µA ≥ µJ Ha: µA < µJ B) Ho: XbarA = XbarJ Ha: XbarA ≠ XbarJ C) Ho: µA ≤ µJ Ha: µA > µJ D) Ho: µA = µJ Ha: µA ≠ µJ

D) Ho: µA = µJ Ha: µA ≠ µJ

An analyst plans to test whether the standard deviation for the time it takes bank tellers to provide service to customers exceeds the standard of 1.5 minutes. The currect null and alterhative hypothesis for this test are: Question options: A) Ho: σ > 1.5 Ha: σ ≤ 1.5 B) Ho: σ ≤ 1.5 Ha: σ > 1.5 C) Ho: σ2 > 2.25 Ha: σ2 ≤ 2.25 D) Ho: σ2 ≤ 2.25 Ha: σ2 > 2.25

D) Ho: σ2 ≤ 2.25 Ha: σ2 > 2.25

Assume you are conducting a one-way analysis of variance using a 0.05 level of significance and have found that the p-value = 0.02. Which of the follow is correct regarding what you can conclude? Question options: A) Reject the null hypothesis; the mean are all the same. B) Do not reject the null hypothesis; the means are all the same. C) Do not reject the null hypothesis; at least some of the means are different. D) Reject the null hypothesis; at least two of the means are different.

D) Reject the null hypothesis; at least two of the means are different.

When a hypothesis test is to be conducted regarding a population variance, the test statistic will be: Question options: A) a binomial distribution p value. B) a t-value from the t-distribution. C) a z-value from the standard normal distribution. D) a Χ2 value from the chi-square distribution.

D) a Χ2 value from the chi-square distribution.

Given the following information, calculate the degrees of freedom(df) that should be used in the pooled-standard deviation t-test. s1/2= 4 s2/2 = 6 n1 = 16 n2 = 25

D) df = 39

Your company wants to compare 3 similar products. One aspect is to test how long the product will last. Product research records 10 samples from each of the three products. A one-way ANOVA test concludes at least one mean is different. What is the q-value that is needed for the Tukey-Kramer test using α = .01α = .01

D) q= 4.55

If a hypothesis test for a single population variance is to be conducted using a significance level of to 0.10, a sample size of n = 16, and the test is a one-tailed upper-tail test, the critical value is: Question options: A) Χ2 = 24.9958. B) t = 1.345. C) z = 1.28. D) Χ2 = 22.3071.

D) Χ2 = 22.3071.

In a one-way ANOVA, which of the following is true? Question options:A) The degrees of freedom associated with the between sum of squares is equal to one less than the number of populations.B) The critical value will be an F-value from the F distribution.C) If the null hypothesis is rejected, it may still be possible that two or more of the population means are equal.D) All of the above.

D) All of the above.

In analyzing the relationship between two numeric variables, a scatter plot can be used to detect which of the following? Question options: A) A positive linear relationship B) A curvilinear relationship C) A negative linear relationship D) No apparent pattern in the scattered points E) All of the options are true

E) All of the options are true

A correlation coefficient (r) of -0.9 indicates a weak linear relationship between the variables.

False

A joint frequency distribution and contingency analysis can only be completed when the original data is quantitative (numeric data).

False

A large tire manufacturing company has claimed that its top line tire will average more than 80,000 miles. If a consumer group wished to test this claim, they would formulate the following null and alternative hypotheses: Ho: μ ≥ 80,000 Ha: μ ≠ 80,000

False

A sample of n observations is taken from a normally distributed population to estimate the population variance. The degrees of freedom for the chi-square distribution are n-2.

False

Given the following sample: Order Total $(x)Tip Amount $(y)9.21 1.50 17.82 3.75 25.85 5.00 32.76 6.50 39.43 8.00 47.32 9.00 73.46 15.00 88.45. 18.00 Is it okay to use the regression equation for x values smaller than $9 and more than $89?

False

If a hypothesis test is conducted for a population mean, a null and alternative hypothesis of the form: Ho: μ = 100 Ha: µ ≠ 100 will result in a one-tailed hypothesis test since the sample result can fall in only one tail.

False

If the R-squared value for a regression model is high, the regression model will necessarily provide accurate forecasts of the y variable. Question

False

If two variables are highly correlated, it not only means that they are linearly related, it also means that a change in one variable will cause a change in the other variable.

False

In a one-way analysis of variance test, the following null and alternative hypotheses are appropriate: Ho: μ1 = μ2 = μ3 Ha: μ1 ≠ μ2 ≠ μ3

False

In conducting one-way analysis of variance, the sample size for each group must be equal.

False