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 Subject: Confidence Interval and Mean Category: Business and Money Asked by: catsabuggin-ga List Price: \$20.00 Posted: 29 Jul 2005 08:06 PDT Expires: 28 Aug 2005 08:06 PDT Question ID: 549391
 ```ABC Corporation of California publishes a variety of statistics, including the number of individuals who got a new job during the past 12 months and the mean length of time the individuals have been on the job. The Statistical Analysis Department of ABC Corporation reported that the mean length of time of newly employed individuals in California was 17.00 weeks. A local Chamber of Commerce for the City of Riverside has commissioned a study on the status of employment in the Riverside area. A sample of 16 employed residents of Riverside included data on the age and the number of weeks on a job. A portion of the data collected in October 2001 is shown as follows: Age Weeks Employed 55 21 30 18 23 11 52 36 41 19 25 12 42 7 45 25 25 6 40 21 25 13 25 11 59 34 49 27 33 18 35 20 a. Based on the above data, summarize the data. Use EXCEL to generate your statistical results. b. Develop a 99% confidence interval estimate of the mean age of newly hired employees. c. How would you determine whether the mean duration of employment in Riverside is greater than the California mean duration of 17.00 weeks. When ? = .01, what is your conclusion? Need this information 2 Aug by 10 p.m.```
 ```Catsabuggin ? You can actually use Excel to do everything required here. A. The quickest way is to have Excel run your descriptive statistics by entering the data, then doing the following: ? click on Data Analysis, then the Descriptive Statistics option ? Click on Summary Statistic; enter the Confidence Interval Level (in decimals, not percentages). Click okay and you?ll get an array of statistics, as shown at the bottom of this spreadsheet linked below: http://www.mooneyevents.com/confidence.xls The 99% confidence level for both age and duration of employment uses an ?alpha? or confidence level of 1% (0.01 in Excel?s statistical format). B. As you can see the confidence interval for AGE is 37.75 years +/- 8.76, so you?re 99% confident that employees being hired are between 28.99 and 45.51 years. Why are the results so bad? There are 5 or almost one-third of our new hires under 25 alone, not just 1%. First, we have a small sample size, which is more prone to errors. But Excel has adjusted for this in using a T-distribution, meant for small sample sizes of under 30. The more fundamental problem is that these statistical tests are designed for ?normal? or bell-shaped distributions. The histogram that I?ve included on the page for ?Age? on this page shows an unusual number of new hires clumped at the bottom and another node in the 41-45 age range. We don?t know why the distribution is skewed ? it may be that the October, 2001 data reflected a large number of recent college graduates. Or that the population of Riverside is mostly young people. But what the test tells us is that it?s a non-normal distribution. Hofstra University ?Confidence Intervals? (Waner & Costenoble, September 2000) http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/finitetopic1/confint.html C. Because the age distribution is poor, it might have an impact on the Weeks Employed. Or it might not. Here, the statistical mean is 18.69 weeks = / - 6.45 weeks or a range of 12.24 to 25.14 weeks at the 99% confidence level. The state average of 17 weeks falls within that range ? so it?s impossible to rule out a hypothesis that Riverside is significantly different than the state data. Here too it?s interesting to look at the histogram of the number of Weeks Employed worked. You can see that, while it?s not a classic bell curve, it?s at least ?closer? to being bell-shaped than the Age graph. The summary statistics at the bottom of the page provide a wealth of information. For example we can see a measure of skew at the bottom of the page ? and positive skew indicates a distribution with an asymmetric tail extending toward more positive values. (Negative skew is a distribution with an asymmetric tail extending toward more negative values.) Similarly kurtosis measures flatness. A positive number says that it looks more like a normal distribution and a negative number says that it is flatter. Google search strategy: ?confidence interval? + ?small sample? + test Best regards, Omnivorous-GA``` Request for Answer Clarification by catsabuggin-ga on 31 Jul 2005 06:48 PDT ```In part C of the question, it ask "how would you determine whether the mean distribution of employment in Riverside is greater than California?" Could you please word that question differently so I can understand how you came to that conclusion? I am clear about the other parts, I had basically the same answers, just did not finsh the problems. Thanks.``` Clarification of Answer by omnivorous-ga on 31 Jul 2005 07:15 PDT ```Catsabuggin -- C. Our statistical mean is 18.69 weeks. If we want to know what range falls within a 99% confidence interval, it's plus or minus 6.45 weeks, as we can see from the 6.448740214 statistic for alpha = .01. That makes it a range of 12.24 to 25.14 weeks at the 99% confidence level. In statistical terms, we'd be asking ourselves, should be be accepting the hypothesis H0 -- that there's no difference in the means of the state and Riverside's mean employment period? Or should we accept H1 -- the assumption that they're different? Statistics Glossary "Hypothesis Testing" http://www.stats.gla.ac.uk/steps/glossary/hypothesis_testing.html They're just too close too assume that Riverside's measure is different from the state's. So Riverside can't reasonably expect to find a cause for length of employment being 1.69 weeks longer in the city -- it just may be the small sample size. And, from a practical standpoint, it may be wise to predict future employees stay 17 weeks, instead of using the 18.69 from its small sample. Those are just some conclusions a manager would reach. On the other hand, a manager might well want to look at why Riverside's hires in October 2001 had so many young people. For example, in an employment discrimination case due to age, this would appear "outside the norm". I know these last 2 paragraphs are nowhere in the scope of your question: I'm simply trying to show the usefulness of the statistics. Best regards, Omnivorous-GA```
 catsabuggin-ga rated this answer: and gave an additional tip of: \$2.00 `Thank you for your answer, I beleive I understand it now.`