Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean
annual consumption of alcoholic beverages by European young women. (to 2 decimals)
a)
Enter your answer using parentheses and a comma, in the form (n1,n2). Do not use commas in your
numerical answer (i.e. use 1200 instead of 1,200, etc.)
For this problem I took the data into excel, and used descriptive analysis tool in the data tool
box. Select descriptive analysis,
SELECT Summary statistics
SELECT confidence level for mean
Enter 95 in confidence level in mean box
Click ok results show…
Mean
130
Standard Error
14.6219013
8
Median
122.5
Mode
93
Standard Deviation
65.3911309
Sample Variance
4276
Kurtosis
0.53641523
7
Skewness

0.15491239
6
Range
266
Minimum
0
Maximum
266
Sum
2600
Count
20
Confidence
Level(95.0%)
30.6039913
1
Now mean ± margin of error
130 ± 30.60 = (99.4,160.6)
=(99.4,160.6)
11) How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10? Assume that the population standard deviation is 40.
12)
Annual starting salaries for college graduates with degrees in business administration are generally
expected to be between $30,000 and $45,000. Assume that a 95% confidence interval estimate of the
population mean annual starting salary is desired. How large a sample should be taken if the desired
margin of error is:
a. $500?
To get
σ we find the range and divide by 4
45,000 – 30,000 = 15,000 / 4 = 7350
7350 / 500 = 14.7 ^2 = 216.09 Round up!
= 217
b. $200?
7350 / 200 = 36.75^2= 1350.56 = 1351
=1351
c. $100?
7350 / 100 = 73.5 ^2 = 5402.25
=5403
d. Would you recommend trying to obtain the $100 margin of error? Explain.
= no, the sample size would probably be too time consuming and costly
13)
Customers arrive at a movie theater at the advertised movie time only to find that they have to sit
through several previews and prepreview ads before the movie starts. Many complain that the time
devoted to previews is too long (
The Wall Street Journal
, October 12, 2012). A preliminary sample
conducted by
The Wall Street Journal
showed that the standard deviation of the amount of time
devoted to previews was four minutes. Use that as a planning value for the standard deviation in
answering the following questions.
a.
If we want to estimate the population mean time for previews at movie theaters with a margin of
error of 75 seconds, what sample size should be used? Assume 95% confidence.
75 / 60 =1.25 margin of error or E =1.25
4 * 1.96 = 7.84 / 1.25 = 6.272 ^2 =39.337984 =40
=40
b.
If we want to estimate the population mean time for previews at movie theaters with a margin of
error of 1 minute, what sample size should be used? Assume 95% confidence.
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 Fall '14
 Statistics, SOLUTIONS, Normal Distribution, Standard Deviation, Homework, Answers , Chapter8, Cengage, GBS, Business Stat