RH1007 Data Analysis and Management Assignment Help
Case Study:
Part A
Texas is home to more than one million undocumented immigrants, and most of them are stuck in low paying jobs. Meanwhile, the state also suffers from a lack of skilled workers. The Texas Workforce Commission estimate that 133,000 jobs are currently unfilled, many because employers cannot find qualified applicants (The Boston Globe, September 29, 2011). Texas was the first state to pass a law that allows children of undocumented immigrants to pay in-state college tuition rate if they have lived in Texas for three years and plan to become permanent residents. The law passed easily back in 2001 because most legislators believed that producing college graduates and keeping them in Texas benefits that business community. In addition since college graduates earn more money, they also provide the state with more revenue. Carol Capaldo wishes to estimate the mean hourly rate of wages of workers with various levels of education. She collects a sample of the hourly wages in $ of 30 workers who did not finish high school.
Using the excel file Texas Wages, report using the following:
1. Calculate descriptive statistics to compare the hourly wages for the three education levels. Then discuss the results by providing interpretation of these using the correct terminology and values.
2. Construct and interpret 95% confidence intervals for the mean hourly wages at each education level.
Part B.
Hypothesis Testing
The data of MPG file shows the miles per gallon (MPG)
1. Calculate descriptive statistics to provide an understanding of MPG first. Provide an interpretation of what the data is stated from the summary.
2. a. State the null and alternative hypothesis in order to test whether the average MPG differs from 95.
2. b. Calculate the value of the test statistic and the p-value
2. c. At a=0.05 can you conclude that the average MPG Differs from 95?
Part C
Statistical Interference with two Populations
Using data of Tractor Times:
1. Calculate descriptive statistics to provide an understanding of Tractor Times first. Provide an interpretation of what the data is stated from the summary.
2. a. Set up the hypotheses to test the claim that the mean assembly time using the new method is less that the old method.
2. b. Calculate the value of the test statistic and the p-value. Assume that population variance are not equal.
c. At the 5% significance level, what is the conclusion.
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Part A
Texas is home to more than one million undocumented immigrants, and most of them are stuck in low paying jobs. Meanwhile, the state also suffers from a lack of skilled workers. The Texas Workforce Commission estimate that 133,000 jobs are currently unfilled, many because employers cannot find qualified applicants (The Boston Globe, September 29, 2011). Texas was the first state to pass a law that allows children of undocumented immigrants to pay in-state college tuition rate if they have lived in Texas for three years and plan to become permanent residents. The law passed easily back in 2001 because most legislators believed that producing college graduates and keeping them in Texas benefits that business community. In addition since college graduates earn more money, they also provide the state with more revenue. Carol Capaldo wishes to estimate the mean hourly rate of wages of workers with various levels of education. She collects a sample of the hourly wages in $ of 30 workers who did not finish high school.
Using the excel file Texas Wages, report using the following:
1. Calculate descriptive statistics to compare the hourly wages for the three education levels. Then discuss the results by providing interpretation of these using the correct terminology and values.
On an average, the person with a bachelor degree will earn more than that with a high school diploma or without a high school diploma. The minimum hourly wage rate for a bachelor degree holder will be $16.85 whereas for a person with no high school diploma will be only $4.62 per hour. The maximum amount of hourly wage, a person without a diploma can is only $15.97 as compared to one with a bachelor degree ($30.53). There is not much variation in the hourly wage rate for a person without a diploma as the basis of education is not there. However, with different education types, there is a high variation in the wage rate of person with a bachelor degree.
2. Construct and interpret 95% confidence intervals for the mean hourly wages at each education level.
Confidence interval for hourly wage for Bachelor’s degree:
95% confidence interval: X ¯±1.96*S/√n
22.96±1.96*3.56/√30
21.69,24.23
Confidence interval for hourly wage for High School Diploma degree:
95% confidence interval: X ¯±1.96*S/√n
12.26±1.96*3.55/√30
10.99,13.53
Confidence interval for hourly wage for No High School Diploma:
95% confidence interval: X ¯±1.96*S/√n
10.46±1.96*2.37/√30
9.61,11.31
Part B.
The data of MPG file shows the miles per gallon (MPG)
1. Calculate descriptive statistics to provide an understanding of MPG first. Provide an interpretation of what the data is stated from the summary.
The mean is 96.52 which means miles per gallon used is 96.52 gallons on an average. The variance is 114.42 which mean there is a high variation in the miles per gallon consumed by different units. The maximum mile per gallon is 117 gallons whereas the minimum is just 78 gallons. The middle value as denoted by median is 96 gallons. Since, mean, median and mode are equal, so the distribution follows a normal distribution.
2. a. State the null and alternative hypothesis in order to test whether the average MPG differs from 95.
Null Hypothesis: The average MPG doesn’t differ from 95 or in other words, the difference between average MPG and 95 is zero.
Alternate Hypothesis: The average MPG differs from 95 or in other words, the difference between average MPG and 95 is not equal to zero.
2. b. Calculate the value of the test statistic and the p-value
Since, mean, median and mode are same, hence the distribution is normal and we can safely use z test.
z=(95-96.52)/(10.69/√25)=-0.7104
P value is 0.4774
2. c. At a=0.05 can you conclude that the average MPG Differs from 95?
Since, p value is greater than 0.05 level of significance, the result is not significant. In other words, we cannot conclude that a significant difference exist. We do not reject the null hypothesis. Hence, there is no difference between the average MPG and 95.
Part C
Using data of Tractor Times:
1. Calculate descriptive statistics to provide an understanding of Tractor Times first. Provide an interpretation of what the data is stated from the summary.
The old method took 32.75 time whereas the new method too slightly less 32.09 on an average. The new method follows a normal distribution as the entire mean, median and mode are equal. The maximum time the old method took was 36 whereas the maximum time is reduced to 35 for the new method. The variations in the two methods are almost same at 3.7. The minimum time to assemble is higher for old method at 30 whereas lower for new method at 29.
2. a. Set up the hypotheses to test the claim that the mean assembly time using the new method is less that the old method.
Null Hypothesis: The mean assembly time using new method is greater than equal to old method.
Alternate Hypothesis: The mean assembly time using new method is less than the neold method.
2. b. Calculate the value of the test statistic and the p-value. Assume that population variance are not equal.
c. At the 5% significance level, what is the conclusion.
At 5% level of significance, 0.07 is greater than 0.05. Hence, we cannot reject the null hypothesis and our result is not significant. In other words, the mean assembly time of new method is not less than the old method.
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