Description
Week 3 assignment
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Submit one Word/PDF file with your answers for all questions and one Excel file to
show your StatTools results.
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Attach StatTools reports (including the user’s name and creation date) that
are specifically asked for in your Word or PDF document.
PROBLEM 1 (15 points)
SmithCo is a supplier to many brand-name makers of mobile phones. SmithCo
manufactures the external shells that enclose mobile phones. The strength of a shell is
measured by applying increasing pressure to the shell and recording the pressure at
which the shell breaks. The shell strength data Download shell strength datafile contains
a random sample of 100 shells made by SmithCo. By hand calculations (use only Excel,
do not use StatTools), construct a 90% confidence interval for the mean shell strength.
1. (3 points) Provide the value of the appropriate Z multiple. Use Excel function
or the following Z values: z0.9 = 1.282, z0.95= 1.645, z0.975 = 1.960, z0.99 =
2.326, z0.995 = 2.576
2. (4 points) Compute the confidence interval in the form point estimate ±
margin of error. Show your work.
3. (4 points) Interpret the confidence interval within the context of the problem.
4. (4 points) What sample size is needed to have 95% confidence of estimating
the mean shell strength to within ± 0.5 pounds.
PROBLEM 2 (25 points)
The ElecMart Download ElecMartfile contains data on 400 customers’ orders from
ElecMart, a company that sells electronic appliances by mail order. The ElecMart wants
to know the effect of ElecMart credit cards. In the data, we assume card type = ElecMart
presents customers who use ElecMart credit card when they make payment and Other
presents customers who don’t use ElecMart credit card.
a. (2 points) Compute the sample proportion of customers who use ElecMart credit
cards.
Hint: You can use pivot table.
b. (4 points) By hand calculations (use only Excel, do not use StatTools), calculate a 95%
confidence interval for the proportion of customers who use ElecMart credit cards.
•
Provide the value of the appropriate Z multiple. Use Excel function or the
following Z values: z0.9 = 1.282, z0.95= 1.645, z0.975 = 1.960, z0.99 = 2.326, z0.995 =
2.576
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Compute the confidence interval in the form point estimate ± margin of error.
Show your work.
Interpret the confidence interval within the context of the problem.
c. (4 points) In part b, the MOE exceeds the target level of 3%. How large should the
sample be if they would like to ensure that MOE is no larger than 0.03 or 3% at 95%
confidence?
Now, we would like to compare total cost of customers who use ElecMart credit card
and don’t use ElecMart credit card. For the purpose of this exercise, we will assume that
total cost is, in general, normally distributed.
d. (3 points) Using Excel, calculate the sample mean and sample standard deviation for
the total cost of customers who use ElecMart credit card and don’t use ElecMart credit
card.
Hint: Use the pivot table to analyze the total cost variable for two categories: “Card Type” =
ElecMart and “Card Type” = Other
e. (4 points) By hand calculation, construct a 95% confidence interval for the average
total cost of customers who use ElecMart credit card. State the confidence interval in
the two forms: point estimate ± margin of error and [lower limit, upper limit]. Interpret
the confidence interval within the context of the problem.
f. (4 points) By hand calculation, construct a 95% confidence interval for the average
total cost of customers who don’t use ElecMart credit card. State the confidence
interval in the two forms: point estimate ± margin of error and [lower limit, upper limit].
Interpret the confidence interval within the context of the problem.
g. (4 points) Discuss the comparison between the total costs of customers who use an
ElecMart credit card and those who do not use one.
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