6
MKTG 460
NOTE FOR EXPERT:
· There are 3 sections with a different dataset in each, use the respective .csv to answer the questions in each section.
· You’ll have to download the .csv’s to analyze, use whatever method you need to use to answer each question (Preferably using R or Excel, but again use whatever)
· Note that there will be some R instructions within this document, again – ignore this if you are using a different method
· Answer all the questions with the symbol & skip any question that is strikethrough
· Simply answer each question on this document, no need for another solution document
· Done in American-English, 500 words total should suffice.
(SECTION 1) Survey Data: Compare Two Means (unpaired or independent groups)
In a popular Dallas, TX mall there are (at least used to be) two (real) Mexican restaurants, Santa Fe Grill (SFG) and Jose’s Southwestern Cafe (JSC). Of particular interest to the SFG owners/managers is how customers perceive their restaurant compared to their direct competition. An interviewer asked customers of these restaurants questions on a (real) marketing survey, of which the actual data are available for your analysis.
The data set includes what is called a screening question, variable name x_s4 in the data set, which asks which restaurant the customer has eaten at most recently, either JSC or SFG, if either.
The interviewer also then asked each customer, among other questions, the following, filling in the blank with either JSC or SFG. The variable name of this response is coded as x22 in the data file.
Full data file:
data: https:
tinyurl.com/3mxdsnsd (use this csv file for this section)
Purpose of analysis: Compare average overall satisfaction levels of SFG customers to JSC customers.
(You will observe a difference in the sample means of satisfaction for the two groups. The question is if this difference that you observe generalizes to the entire population of potential customers.)
Answer with questions a-z on the Template for the Analysis of a Mean Difference, except for those crossed out, which are not part of this class.
Input
R statement to obtain the analysis.
Describe the Data
Identify the grouping variable and the response variable in this analysis according to its
i. Ve
al description, the meaning of each variable
· Grouping variable:
· Response variable:
ii. Variable name, as it appears in the first row of the data table. Each variable in a data table is named in the first row of the data table, usually less than 8 or 10 characters. #3,4,30]
· Grouping variable:
· Response variable:
Specify the types of data values in the data file for each of the two variables. Provide an example data value for each variable.
· Grouping variable:
· Response variable (can be hypothetical):
How many data values are in each group (sample) of responses?
·
Show the computations of the sample mean difference using the numbers from this specific analysis. Which group scored higher than the other?
·
Within-group variability (standard deviation).
Assumptions
Evaluate the assumption for a stable process
·
Evaluate the assumption of the normality of the sample mean difference, if possible.
·
Evaluate the assumption of homogeneity of variance.
Hypothesis Test
Standard e
or of mean difference.
Degrees of freedom.
Specify the null hypotheses and its alternative for the mean difference with respect to the specific variables in this analysis.
·
Specify the cutoff (critical) values that set the 95% range of variation of the t-statistic for the sample mean difference.
·
Specify the computations of the t-value by applying the relevant numbers from this specific analysis. No need to compute anything. [1 pt]
·
Specify the definition of the p-value as applied to the numbers from this specific analysis.
·
Specify the basis for the statistical decision regarding the hypothesis test and the resulting statistical conclusion.
·
HT: Interpretation, as an executive summary that you would report to management.
·
Recommend, if any, follow-up analyses. Why?
Confidence Interval
Specify what it is that the confidence interval estimates.
·
Specify the computation of the margin of e
or by applying the relevant numbers of this specific analysis.
·
Show the computations of the confidence interval illustrated with the specific numbers from this analysis.
·
CI: Interpretation, as an executive summary that you would report to management.
·
Needed sample size at .90 probability to obtain the desired margin of e
or for a 95% CI.
Effect Size
Show the computations of the standardized mean difference (smd) using the numbers from this specific analysis.
smd: Interpretation, as you would report to management.
Conclusion
Demonstrate the consistency of the confidence interval and hypothesis test using the specific numbers for this analysis for both results. Explain why.
·
What managerial decision do you recommend to management based on these findings?
[describe why this study was done and the decision that you would implement givens results, explained in language that is relaxed without any jargon, as if you were explaining your results to upper management who could care less or not understand the technical issues]
·
(SECTION 2) Advertising Claim: Compare Two Means (unpaired or independent groups).
Our company makes paint, and so does our primary competitor. Our company would like to advertise that our paint dries faster than our competitors. To investigate, our company tested two different paints, each with several different trials, and measured the Dry Time for each trial. Compare the means of Dry Time for Brand Ours and Brand Theirs in hours.
The sample means of Dry Time for Brand Ours and Brand Theirs differ. No surprise, because the sample means of the groups always differ. Is this difference due only to chance, with equal co
esponding population means? Or do these unknown population means of Dry Time differ? If so, what is the extent of this true difference?
Data: https:
tinyurl.com
deec6zc (use this csv file for this section)
Purpose of analysis: Compare the means of Dry Time for Brand Ours and Brand Theirs in hours.
(You will observe a difference in the sample means of paint dry time for the two groups. The question is if this difference that you observe generalizes to the entire population of potential paint made by the two companies.)
Answer with questions a-z on the Template for the Analysis of a Mean Difference, except for those crossed out.
Input
R statement to obtain the analysis.
Describe the Data
Identify the grouping variable and the response variable in this analysis according to its
i. Ve
al description, the meaning of each variable
· Grouping variable:
· Response variable:
ii. Variable name, as it appears in the first row of the data table. Each variable in a data table is named in the first row of the data table, usually less than 8 or 10 characters.
· Grouping variable:
· Response variable:
Specify the types of data values in the data file for each of the two variables. Provide an example data value for each variable.
· Grouping variable:
· Response variable (can be hypothetical):
How many data values are in each group (sample) of responses?
·
Show the computations of the sample mean difference using the numbers from this specific analysis. Which group scored higher than the other?
·
Within-group variability (standard deviation).
Assumptions
Evaluate the assumption for a stable process
·
Evaluate the assumption of the normality of the sample mean difference, if possible.
·
Evaluate the assumption of homogeneity of variance.
Hypothesis Test
Standard e
or of mean difference.
Degrees of freedom.
Specify the null hypotheses and its alternative for the mean difference with respect to the specific variables in this analysis.
·
Specify the cutoff (critical) values that set the 95% range of variation of the t-statistic for the sample mean difference.
·
Specify the computations of the t-value by applying the relevant numbers from this specific analysis. No need to compute anything.
·
Specify the definition of the p-value as applied to the numbers from this specific analysis.
[apply the definition of the p-value to the relevant numbers in this specific
·
Specify the basis for the statistical decision regarding the hypothesis test and the resulting statistical conclusion.
[specific with the numbers from this analysis as to the evaluation of the null hypothesis]
·
HT: Interpretation, as an executive summary that you would report to management.
·
Recommend, if any, follow-up analyses. Why?
Confidence Interval
Specify what it is that the confidence interval estimates.
·
Specify the computation of the margin of e
or by applying the relevant numbers of this specific analysis.
·
Show the computations of the confidence interval illustrated with the specific numbers from this analysis.
·
CI: Interpretation, as an executive summary that you would report to management.
·
Needed sample size at .90 probability to obtain the desired margin of e
or for a 95% CI.
Effect Size
Show the computations of the standardized mean difference (smd) using the numbers from this specific analysis.
smd: Interpretation, as you would report to management.
Conclusion
Demonstrate the consistency of the confidence interval and hypothesis test using the specific numbers for this analysis for both results. Explain why.
·
What managerial decision do you recommend to management based on these findings?
·
(SECTION 3) Compare Differences of Matched Scores (paired or dependent samples)
A telephone company claimed that by switching to its services, costs would decrease. To evaluate this claim, the manager who made the decision to adopt the new phone company had samples of the last 8 monthly company phone bills analyzed, which were then compared monthly to the actual costs using the cu
ent phone company.
Data: https:
tinyurl.com/2shr3fhy (use this csv file for this section)
I. To understand what is being analyzed, not part of the usual data analysis, directly observe the difference scores to compare costs of the two phone systems.
i) From the data file on the web, create the new variable of the difference scores. To refer to a variable, need to include both the data frame name and the variable name. To identify a variable, prefix the variable name with the name of the data frame, and then $, such as d$ for data frame d. Create a new, transformed variable by directly entering into the R console the equation that defines the new variable.
d$Diff <- d$New – d$Cu
ent
To see better what this preceding statement accomplishes, list the variable names and data after the transformation by entering d, such as with head(d). You will see the new variable Diff in the data frame.
ii) As you view these transformed data values, just by looking at the data does it appear that the new phone system is cheaper? Why or why not?
II. For the formal data analysis with statistical inference to evaluate the effectiveness of the new phone system, directly compare the differences in costs between the two phone systems to the inferential analysis directly of the differences.
Input
R statement to obtain the analysis.
Preliminaries
a. Evaluate the assumption of the normality of the means for the two groups.
·
. Specify the degrees of freedom.
·
c. Estimated standard e
or of sample mean. Show calculations.
·
Hypothesis Test
d. Specify the null hypothesis and its alternative with respect to the specific variables in this analysis.
·
e. Specify the computations of the t-statistic (i.e., t-statistic) by applying the relevant numbers from this specific analysis.
[show the definition of the concept by applying the relevant numbers of this specific analysis, either providing the formula or describe the formula in words]
·
f. Specify the definition of the p-value as applied to this specific analysis.
[apply the definition of the p-value to the relevant numbers in this specific analysis]
·
g. Specify the basis for the statistical decision and the resulting statistical conclusion.
[the basis for the decision regarding the null hypothesis]
·
h. HT: Interpretation, as you would report to management.
[applied to the relevant numbers of this specific analysis, with no jargon like p-value or t-value]
·
i. Recommend, if any, follow-up analyses. Why?
Confidence Interval
j. Specify the value the confidence interval estimates.
[do not provide the confidence interval; which is the estimate not the value estimated]
·
k. Specify the computation of the margin of e
or by applying the relevant numbers of this specific analysis.
[show the definition of the concept by applying the relevant numbers of this specific analysis, either providing the formula or describe the formula in words]
·
l. Show the computations of the confidence interval illustrated with the specific numbers from this analysis.
[show the definition of the concept by applying the relevant numbers of this specific analysis, either providing the formula or describe the formula in words]
·
m. CI: Interpretation, as you would report to management.
[no jargon, which includes the phrase “mean difference”, nothing about hypothesis tests, which is another question]
·
n. Needed sample size at .90 probability of obtaining the desired margin of e
or.
o. Interpretation of needed sample size.
Conclusion
p. Demonstrate the