Answer the question about business analytic for decision making (Calculations)

All the questions are given in the attachment below. Please finish it as careful as possible. Explain each question how you make it ( including references if needed)This is one example:5.In 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent (Pew Research, June 5, 2014). An independent research firm has been charged with conducting a sample survey to obtain more current information.a. What sample size is needed if the research firm’s goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of .03? Use a 95% confidence level.b. Repeat part (a) using a 99% confidence level.
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Midterm Examination
Answer all questions. All work must be shown to qualify for partial credit.
1.
Consumer Reports posts reviews and ratings of a variety of products on its website. The
following is a sample of 20 speaker systems and their ratings. The ratings are on a scale of 1 to 5, with 5
being best.
Speaker
Rating
Infinity Kappa. 6.1
4.00
ACI Sapphire III
4.67
Allison One
4.12
Bose 501 Series
2.14
Cambridge Ensemble II
3.82
DCM KY-212
4.09
Dynaudio Contour 1.3
4.00
Eosone RSF 1000
4.17
Hsu Rsch. HRSW 12V
4.56
Joseph Audio RM7 si
4.88
Legacy Audio Focus
4.32
Martin Logan Aerius
4.26
Mission 73Ii
4.33
Omni Audio SA 12.3
2.32
PSB 400i
4.50
Polk Audio RT 12
4.50
Snell Acoustics D IV
4.64
Sunfire True Subwoofer
4.17
Thiel CS 1.5
4.20
Yamaha NS- A636
2.17
a.
b.
c.
d.
e.
f.
Speaker
Rating
Compute the mean and the median.
Compute the first and third quartiles.
Compute the standard deviation.
The skewness of this data is – 1.67. Comment on the shape of the distribution.
What are the z-scores associated with Allison One and Omni Audio?
Do the data contain any outliers? Explain.
2.
2.
Fewer young people are driving. In 1983, 87% of 19-year-olds had a driver’s license.
Twenty-five years later that percentage had dropped to 75% (University of Michigan Transportation
Research Institute Website, April 7, 2012). Suppose these results are based on a random sample of 1200
19-year-oldes in 1983 and again in 2008.
a. At 95% confidence, what is the margin of error and the interval estimate of the number of 19-year-old
drivers in 1983?
1
b. At 95% confidence, what is the margin of error and the interval estimate of the number of 19-year-old
drivers in 2008?
c. Is the margin of error the same in parts (a) and (b)? Why or why not?
3.
Consumption of alcoholic beverages by young women of drinking age has been increasing in the
United Kingdom, the United States, and Europe (The Wall Street Journal, February 15, 2006). Data
(annual consumption in liters) consistent with the findings reported in The Wall Street Journal article are
shown for a sample of 20 European young women.
266
82
199
174
97
170
222
115
130
169
164
102
113
171
0
93
0
93
101
130
Assuming the population is roughly symmetric; construct a 95% confidence interval for the mean annual
consumption of alcoholic beverages by European young women.
4.
Disney’s Hannah Montana: The Movie opened on Easter weekend in April 2009. Over the threeday weekend, the movie became the number-one box office attraction (The Wall Street Journal, April
13, 2009. The ticket sales revenue in dollars for a sample of 25 theaters is as follows.
20,200
10,150
13,000
11,320
9700
8350
7300
14,000
9940
11,200
10,750
6240
12,700
7430
13,500
13,900
4200
6750
6700
9330
13,185
9200
21,400
11,380
10,800
a. What is the 95% confidence interval estimate for the mean ticket sales revenue per theater?
Interpret this result.
b. Using the movie ticket price of $7.16 per ticket, what is the estimate of the mean number of
customers per theater?
c. The movie was shown in 3118 theaters. Estimate the total number of customers who saw
Hannah Montana: The Movie and the total box office ticket sales for the three day weekend.
5.
In 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent (Pew
Research, June 5, 2014). An independent research firm has been charged with conducting a sample
survey to obtain more current information.
2
a. What sample size is needed if the research firm’s goal is to estimate the current proportion of homes
with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of .03?
Use a 95% confidence level.
b. Repeat part (a) using a 99% confidence level.
3

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