Each month the U.S. Bureau of Labor Statistics publishes a variety of unemployme

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 14.6 weeks. Please conduct hypothesis testing with 0.01 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 Mean 36.6 15.54 Standard Error 1.689342343 1.403846029 Median 34 13.5 Mode 27 7 Standard Deviation 11.94545426 9.926690469 Sample Variance 142.6938776 98.53918367 Kurtosis -1.145149979 0.053711356 Skewness 0.357283468 0.9107658 Range 39 38 Minimum 20 1 Maximum 59 39 Sum 1830 777 Count 50 50

Explanation / Answer

1. Ans to 1 is already given.

2. The sample size is large, and population standard deviation is unknown. Use Student's t model to cocmpute the 90% c.i for true population mean age of unemployed individuals is as follows:

xbar+-talpha/2, df=n-1 (s/sqrt N), where, xbar is sample mean, t is t critical at alpha/2, and df=n-1, s is sample standard deviation, and N is sample size.

=36.60+-1.67655(11.95/sqrt 50)

=(33.77, 39.43)

3. The 95% c.i for true population mean number of weeks of unemployment in the city is as follows:

xbar+-talpha/2, df=n-1 (s/sqrt N)

=15.54+-2.0096(9.93/sqrt 50)

=(12.72, 18.36)

4. Hypotheses: H0: mu<=14.6 (population mean duration of unemployment in the city is atmost 14.6 weeks)

H1:mu>14.6 (population mean duration of unemployment in the city is greater than 14.6 weeks)

For large sample size, n>30, and unknown population standard deviation, use students't t model to compute 1-sample t test statistic.

t=(xbar-mu)/(s/sqrt n), where, xbar is sample mean, mu is population mean, s is sample standard deviation, and n is sample size.

=(15.54-14.6)/(9.93/sqrt 50)

=0.67

p value at 49 degrees of freeom [df=n-1] is:0.253.

Conclusion: Per rule, reject H0, if p value is less than 0.01. Here, p value is not less than 0.01, therefore, fail to reject H0. There is insufficient sample evidence to warrant the rejection of null hypothesis or mayor's claim.

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