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Analytical Reviews

Statistical Problems

Statistics Exam Questions

View Solution # 27126

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PROBLEM 1:
For each of the following claims mention what kind of test should be used (one-tail, two-tail) and set up the null and alternate hypothesis.
a) The Pastry shop claims that its chocolate cookies have at least 60% chocolate per cookie.
b) The 87Cents Store claims that their daily profit is at least $1,000.
c) The Feather baggage store claims that its BlueSky brand luggage weights exactly 1.5 pounds.
d) Coffee and Tea shop claims that their Latté always scores a 9 on a (non-integral) scale of 1-10.

PROBLEM 2:
A supplier manufactures batteries for the emergency backup lights in the mall corridors. A random sample of 256 batteries is taken and the sample mean life is 6.5 years with a standard deviation of 0.65 years. The law requires 99% confidence of operation when scheduling of battery replacement.
a) If The McDonald wants to be at his safest, he should replace the batteries at: (the lower-limit on a two-sided confidence interval)
b) If The McDonald wants to be cheap frugal, but within the law, he should replace the batteries no later than: (the upper-limit on a two-sided confidence interval)

PROBLEM 3:
Mall security estimates that the average daily per-store theft is exactly $335, but wants to determine the accuracy of this statistic. The company researcher takes a sample of 81 clerks and finds that =$300 and s = $80.
a) Test at a = 0.05.
b) Construct a 95% CIE of µ

PROBLEM 4:
A confidence interval of 90% was used to estimate the proportion of customers who buy at least two items during their shopping mall experience. A random sample of 150 customers produced the following confidence interval: 32% +/- 4%. What is the best way to explain the results?

PROBLEM 5:
In your own words, when you should use a z-test versus a t-test?

PROBLEM 6:
Thump wants his apprentices to stand on the street with signs claiming that mall shoppers live longer.
Mall Shoppers   Non-Mall Shoppers
Is this claim supported by the data?
a) Test at ? =.01
b) Test at ? =.10
c) Does this statistic truly instill confidence in you?

PROBLEM 7:
Who misses work more often at the Sinnabon (bun rollers or pretzel bakers)? Test at .05 significance level.
Bun Rollers: Average number of days absent = 13.9; standard deviation = 4.85; n = 44
Pretzel Bakers: Average number of days absent = 8.7; standard deviation = 4.40; n = 60

PROBLEM 8:
Who carries cheaper televisions West Buy or Village Short-Circuit? Test at .05 significance level
West Buy: Average price = $705.00; standard deviation = 150.0; n = 12
Village Short-Circuit: Average price = $665.00; standard deviation = 100.0; n = 18

PROBLEM 9:
Who abuses customers more often: credit card solicitors or nail-care booth sales-staff? Test at .05 significance level.
Credit card solicitors: Average number of complaints per day = 10.9 complaints; standard deviation = 2.4 complaints; n = 10
Nail-care booth sales-staff: Average number of complaints per day = 9.9 complaints; standard deviation = 1.8 complaints; n = 20

PROBLEM 10:
A company has a set of data with employee age (X) and the corresponding number of annual on-the-job-accidents. Analysis on the set finds that the regression equation is Y=115-3.78X.
What can be said of the correspondence between age and accidents?
Are older workers safer or more prone to accident?
What is the likely number of accidents for someone aged 25?
What does the slope tell you about accidents relative to age?

PROBLEM 11:
Victor’s Announcement, a hunting store, is interested in providing cashiers guidelines for speed of service. A random sample of 18 employees is used for this process.
Average Number of Items in Customer Cart Number of Transactions per Hour
10.0   26
9.7   26.5
9.4   31
9.2   35
9.0   38
8.8   39
8.5   40
8.3   40
8.2   42.5
8.0   43
7.9   45
7.5   47
7.3   50
7.1   51
6.8   55.5
6.5   60
6.2   67.5
5.0   81
a) What are the mean and median transactions per hour for the 18 employees?
b) A manager at the firm feels that the number of transactions per hour is related to the number of items in a customer’s cart. (Note: this is an exceptionally perceptive, high-paid manager.) He feels that employees who have lines with smaller average order sizes ought to be able to do the job faster.   Does the data support his hunch?

PROBLEM 12:
The McDonald has several employees roaming the mall marketing credit cards. To best determine what age group to target aggressively, data was collected related to the age of shoppers versus the number of credit cards they’ve already “maxed out”.
Age   Number of Credit Cards
16   4
16   7
17   3
18   8
18   5
19   7
20   9
21   4
21   8
22   10
23   10
23   9
a.Calculate the following statistically useful quantities.
EX
EY
EXY
EX2
EY2
b.Calculate the correlation coefficients.
R
R2
c.Is there a strong correlation?
d.Describe the line of regression (in Y=mX+b format)
e.Depict the data on a scatter plot.
f.What does the regression line formula tell you about the data? What should the marketers conclude?

Solution

The answers to all the 12 questions along with complete calculations and steps are provided in the solution.

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Price: $25.00