Sunday, April 11, 2010

Statistics Assignment #2 [MBA]

Problem 1

For this assignment, use the internet site usage data that is listed in Table 11.1.3 on page 441 in the textbook. It is in the data file for Chapter 11.

a. Based on this date, make a 95% interval estimate of the average time spent on line at all internet sites.

Confidence interval for time spent on line at all internet sites: We are 95% sure that the population mean for time spent on line at all internet sites is somewhere between 11.906 and 28.990 (assuming a random sample from a normal population).


b. If you wanted to reduce the width of this 95% interval to ± 4 minutes, what can you do? Be as specific as you can!

If I understand the question correctly, in order to get the interval within an 8-minute interval range while maintaining a 95% confidence level, we would need to increase the number of sites tested, thus increasing “n” and “degrees of freedom” to yield a higher value.

If we can lower the confidence level, we could keep the number of sites the same and lower the confidence level to about 70%.

c. When StatPad produces a one-sample confidence interval (which you could have used in your answer to part a), it ends with a statement about assumptions “(assuming .... )”. Do those assumptions appear valid here?

No, one of the assumptions is that the sample is random, but the sites are the top 25 global web properties accessed at home, so are therefore not random

Problem 2

For this problem, use the data from Problem 25 in Chapter 10 (page 422). Produce a 95% lower bound for the average satisfaction level.

One-sided upper confidence interval for the average satisfaction level: We are 95% sure that the population mean for the satisfaction level is at least 75.666 (assuming a random sample from a normal population).

The company wants a minimum satisfaction level of 80. Does your result indicate this level is likely to be met?


Null hypothesis
H0: u >_ u0
H0:u>_80
Research hypothesis
H1: u
H1:u<80
Average
X
83.25
Standard Error
Sx
4.223177
Reference Value
u0
80
t statistic
X-u0/Sx
0.769563
Critical Value
ttable
1.796
Decision
Accept Accept H0



Because the t statistic is not greater than the t table,


we do not have significant evidence that proves


the null hypothesis is unreasonable




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