Each month the U.S. Bureau of Labor Statistics publishes a variety of unemployme
ID: 3362511 • Letter: E
Question
Each month the U.S. Bureau of Labor Statistics publishes a variety of unemployment statistics, including the number of individuals who are unemployed and the mean length of time the individuals have been unemployed. The mayor of a city has requested a study on the status of unemployment in the city. A sample of 50 unemployed residents of the city included data on the age and the number of weeks without a job. The data collected are available in the data set BLS. The managerial report should contain such as:
1. Use MS Excel Descriptive Statistics to summarize age and number of unemployment weeks.
2. Develop a 90% confidence interval estimate of the mean age of unemployed individuals in the city. You have to show the interval formula and calculation process.
3. Develop a 95% confidence interval estimate of the mean number of weeks of unemployment in the city. You have to show the interval formula and calculation process.
4. The mayor claims that the mean duration of unemployment in the city is not greater than the national mean duration of 13.8 weeks. Please conduct hypothesis testing with 0.10 level of significance. What is your conclusion?
5. Is there a relationship (trend) between the age of an unemployed individual and the number of weeks of unemployment? If so, please show the tool (graph or statistic) to prove it.
Age Weeks 56 22 35 19 22 7 57 37 40 18 22 11 48 6 48 22 25 5 40 20 25 12 25 1 59 33 49 26 33 13 56 15 20 17 31 11 27 17 23 3 45 17 29 14 31 4 59 39 39 7 35 12 44 38 27 14 24 6 27 7 45 25 42 33 45 16 44 12 21 13 31 16 42 4 23 14 51 31 27 7 30 10 33 23 32 8 22 7 51 12 50 16 21 9 38 5 26 8 55 35Explanation / Answer
5.331177 when in excel z=test is applied maximum value is coming out to be maximum12.41 weeks at 90% confidence level. so the mayor's claim is true.
2) zat90%= 1.645 =population mean+ sample mean/
(1.645*13.58)+40=population mean (upper limit) =66.3391
40-(1.645*13.58)=population mean (lower limit)= 17.66
3)zat 95%=1.96=population mean+sample mean/
(1.96*10)+16.68 =population mean =36.28(upper limit)
(1.96*10)-16.68=2.92
age weeks Mean 40 Mean 16.6875 Standard Error 3.396076167 Standard Error 2.501198 Median 40 Median 16.5 Mode 25 Mode 22 Standard Deviation 13.58430467 Standard Deviation 10.00479 Sample Variance 184.5333333 Sample Variance 100.0958 Kurtosis -1.588932176 Kurtosis -0.19736 Skewness -0.016412782 Skewness 0.452765 Range 37 Range 36 Minimum 22 Minimum 1 Maximum 59 Maximum 37 Sum 640 Sum 267 Count 16 Count 16 Confidence Level(95.0%) 7.238564975.331177 when in excel z=test is applied maximum value is coming out to be maximum12.41 weeks at 90% confidence level. so the mayor's claim is true.
2) zat90%= 1.645 =population mean+ sample mean/
(1.645*13.58)+40=population mean (upper limit) =66.3391
40-(1.645*13.58)=population mean (lower limit)= 17.66
3)zat 95%=1.96=population mean+sample mean/
(1.96*10)+16.68 =population mean =36.28(upper limit)
(1.96*10)-16.68=2.92
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