AAA Co. operates distribution centers in the Midwest. Three of their centers were
recently audited to determine if they are in compliance with company standard billing
procedures. According to the auditing firm, a billing had an equal probability of being
from each of the three centers. A random sample of the audited billings had the
following distribution:
What is the critical value at α = .01 to test the null hypothesis (equal billings from each
center)?
On the most recent tax cut proposal, a random sample of Democrats and Republicans in
the Congress cast their votes as follows:
Determine the expected frequencies for both the Democrats and Republicans who
oppose the tax cut proposal for the chi-square test of independence.
Consider a two-way analysis of variance experiment with treatment factors A and B.
The results are summarized below.
If the mean response for level 1 of Factor A is 31.5 and the mean response of level 2 of
Factor A is 22.5, calculate a Tukey simultaneous 95 percent confidence interval for this
difference.
A local tire dealer wants to predict the number of tires sold each month. He believes
that the number of tires sold is a linear function of the amount of money invested in
advertising. He randomly selects 6 months of data consisting of monthly tire sales (in
thousands of tires) and monthly advertising expenditures (in thousands of dollars).
Residuals are calculated for all of the randomly selected six months and ordered from
smallest to largest. Determine the normal score for the third residual in the ordered
array.
A manufacturing company produces part A732 for the aerospace industry. This
particular part can be manufactured using 3 different production processes. The
management wants to know if the quality of the units of part A732 is the same for all
three processes. The production supervisor obtained the following data: Process 1 had
29 defective units in 240 items, Process 2 produced 12 defective units in 180 items, and
Process 3 manufactured 9 defective units in 150 items. At a significance level of .05,
the management wants to perform a hypothesis test to determine whether the quality of
items produced appears to be independent of the production process used. Calculate the
expected number of conforming units produced by Process 2.
A local tire dealer wants to predict the number of tires sold each month. He believes
that the number of tires sold is a linear function of the amount of money invested in
advertising. He randomly selects 6 months of data consisting of tire sales (in thousands
of tires) and advertising expenditures (in thousands of dollars). Based on the data set
with 6 observations, the simple linear regression model yielded the following results.
Calculate the sample correlation coefficient.
Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and
with the following observed frequencies.
It is desired to test whether these measurements came from a normal population.
Calculate the expected frequency for the interval 60-79.99.
Looking at four different diets, a researcher randomly assigned 20 equally overweight
women into each of the four diets. What are the degrees of freedom for the error?
Consider the following one-way ANOVA table.
What is the value of the F statistic?
Consider the 3 2 contingency table below.
At α = .05, determine the tabular value of the chi-square statistic used to test for the
independence of Factors A and B.
A local tire dealer wants to predict the number of tires sold each month. He believes
that the number of tires sold is a linear function of the amount of money invested in
advertising. He randomly selects 6 months of data consisting of monthly tire sales (in
thousands of tires) and monthly advertising expenditures (in thousands of dollars).
Residuals are calculated for all of the randomly selected six months and ordered from
smallest to largest. Determine the normal score for the smallest residual.
A particular multiple regression model has 3 independent variables, the sum of the
squared error is 7680, and the total number of observations is 34. What is the value of
the standard error of estimate?
A local tire dealer wants to predict the number of tires sold each month. He believes
that the number of tires sold is a linear function of the amount of money invested in
advertising. He randomly selects 6 months of data consisting of tire sales (in thousands
of tires) and advertising expenditures (in thousands of dollars). Based on the data set
with 6 observations, the simple linear regression model yielded the following results.
Find the rejection point for the t statistic at α = .05 and test H0: β1 ≤ 0 vs. Ha: β1 > 0.
Consider the one-way ANOVA table.
If there are an equal number of observations in each group, then each group (treatment
level) consists of how many observations?
Below is a partial multiple regression ANOVA table.
What is the mean square error?
The following results were obtained from a simple regression analysis:
Ŷ = 37.2895 – (1.2024)X
r2 = .6744sb = .2934
What is the proportion of the variation explained by the simple linear regression model?
Below is a partial multiple regression computer output based on a quadratic regression
model.
Test the usefulness of the variable X in the model at α = .05.
Consider the 3 2 contingency table below.
How many degrees of freedom are associated with the chi-square test?