Holly Teal

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Background: The claims manager at All Stated was interested in seeing if there was a difference in how long male customers stayed with the company as compared to women. A sample of 13 males and 13 females was collected. The goal is to create a 90% confidence interval to gauge the difference.

Method: Use the sample data and Excel PhStat to run an analysis and create a 90% confidence level.

Analysis:

Data / Mean / Stdev
Males / 14 / 9 / 9 / 16 / 14 / 8 / 12 / 11 / 6 / 9 / 10 / 7 / 3 / 9.85 / 5.31
Females / 3 / 10 / 4 / 7 / 10 / 5 / 4 / 1 / 4 / 4 / 6 / 9 / 2 / 3.58 / 2.93

To use a 90% confidence interval , we are going to assume the data is normally distributed. Running an F-Test on the variances with the sample data and a significance of .05, we were not able to prove there was a difference in the variances. Therefore, we will assume the variances are equal.

The following is output from PHStat for a 90% confidence level. This was done by running a pooled

t-test on two means and selecting the confidence interval.

The hypothesis test would be as follows:

Ho: Mean for males = Mean for females
Ho: Mean for males ≠ Mean for females
alpha = .10 with a 90% confidence level
t Test Statistic / 3.4617
Two-Tail Test / Confidence Interval
Lower Critical Value / -2.0639 / Interval Lower Limit / 2.344803642
Upper Critical Value / 2.0639 / Interval Upper Limit / 6.732119435
p-Value / 0.0020
Reject the null hypothesis
The means are not equal. Looking at the raw averages, mean are more than women.

Statistical Conclusion: The hypothesis test showed there was a difference between males and females. Based on the sample, we can be 90% confident that the difference is between 2.3 to 6.7 years. Looking at the raw averages, males stay longer than females.

Executive Business Summary: Based on the sample, the western region claims manager can be 90% confident that males stay 2.3 to 6.7 years longer than females customers. Knowing this can lead the manager to consider marketing options. A further study to determine why there is such a gap would be of interest. Are other companies ads more appealing to women? Do we have customer service issues? Is this trend the same at other companies? While this fact alone is helpful, it does lead to many other questions.