Carpetland salespersons average $8,000 per week in sales.
Steve Contois, the firm’s vice president, proposes a compensation
plan with new selling incentives. Steve hopes that the results of a
trial selling period will enable him to conclude that the compensation
plan increases the average sales per salesperson.
A.Develop the appropriate null and alternative hypotheses.
B.What is the Type I error in this situation? What are the consequences
of making this error?
C.What is the Type II error in this situation? What are the consequences
of making this error?
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>Individuals filing federal income tax returns prior to March 31 received an average
refund of $1,056. Consider population of “last minute” filers who mail their tax return
during the last five days of the income tax period (typically April 10 to 15).
A.A researcher suggests that a reason individuals wait until the last five days is that on average
these individuals receive lower refunds than do early filers. Develop appropriate hypotheses
such that rejection of H(o) will support the researcher’s contention.
B.For a sample of 400 individuals who filed a tax return between April 10-15, the sample
mean refund was $910. Based on prior experience, a population standard deviation of
o = $1,600 may be assumed. What is the p-value?
C.At a = .05, what is your conclusion?
D.Repeat the preceding hypothesis test using the critical value approach.
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>Commercial real estate prices and rental reates suffered substantial declines
in the past year (Newsweek article July 2009). These declines were particularly
severe in Asia; annual lease rates in Tokyo, Hong Kong, and Singapore declined
by 40% or more. Even with such large declines, annual lease rates in Asia were
still higher than in many cities in Europe and the United States. Annual lease
rates for a sample of 30 commercial properties in Hong Kong showed an average
of $1,114 per square meter with a standard deviation of $230. Annual lease rates
for a sample of 40 commercial properties in Paris showed an average lease rate of
$989 per square meter with a standard deviation of $195.
A.On the basis of the sample results, can we conclude that the mean annual lease rate
is higher in Hong Kong than in Paris? Develop appropriate null and alternative hypotheses.
B.Use a = .01. What is your conclusion? Are rental rates higher in Hong Kong than in Paris?
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>Airline travelers often choose which airport to fly from based on flight cost.
Cost data (in dollars) for a sample of flights to eight cities from Dayton, Ohio
and Louisville, Kentucky were collected to help determine which of the two
airports was more costly to fly from (2006 study). A researcher argued that it is
significantly more costly to fly out of Dayton than Louisville. Use the sample data to
see whether they support the researcher’s argument. Use a = .05 as the level of significance
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>The above data give the percentage of women working in five companies
in the retail and trade industry. The percentage of management jobs held
by women in each company is also shown.
A.Develop a scatter diagram for these data with the percentage of women working
in the company as the independant variable.
B.What does the scatter diagram developed in part (a) indicate about the relationship
between the two variables?
C.Try to approximate the relationship between the percentage of women working
in the company and the percentage of management jobs held by women in that company.
D.Develop the estimated regression of equation by computing the values of B(o) and B(v).
E.Predict the percentage of management jobs held by women in a company that has
60% women employees.
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>The estimated regression equation for these data is? = 7.6 + .9x.
What percentage of the total sum of squares can be accounted
for by the estimated regression equation? What is the value of the
sample correlation coefficient?
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>A.Develop a scatter diagram with weight as the independent variable.
B.Does there appear to be any relationship between these two variables?
C.Develop the estimated regression equation that could be used to predict
the price given the weight.
D.Test for the significance of the relationship at the .05 level of significance.
E.Did the estimated regression equation provide a good fit? Explain.
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>The following 2 X 3 contingency table contains observed frequencies for a sample
of 200. Test for independence of the row and column variables using the x (2) test
with a = .05.
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>The Goodman Tire and Rubber Company periodically tests its tires for tread wear under
simulated road conditions. To study and control the manufacturing process, 20 samples,
each containing three radial tires, were chosen from different shifts over several days of
operation, with the following results. Assuming that these data were collected when the
manufacturing process was believed to be operating in control, develop the R and ? charts.
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>An automotive industry supplier produces pistons for several models of automobiles.
Twenty samples, each consisting of 200 pistons, were selected when the process was
known to be operating correctly. The numbers of defective pistons found in the samples
follow.
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”>A quality control process monitors the weight per carton of laundry detergent.
Control limits are set at UCL = 20.12 ounces and LCL = 19.90 ounces. Samples of size 5 are used for the
sampling and inspection process. What are the process mean and process standard
<pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=”” style=”font-family: Verdana, arial, sans-serif; line-height: normal;”><pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=””><pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=””><pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=””><pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=””><pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=””><pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=””><pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=””><pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=””><pstyle=”language:en-us;margin-top:0pt;margin-bottom:0pt;margin-left:0in; text-indent:0in”=””>
deviation for the manufacturing operation?
