The dataset MLB contains salary data for Major League Baseball players in the ye

Question

The dataset MLB contains salary data for Major League Baseball players in the year 2010. The dataset has 828 observations on the following four variables: player: Player name team: Team position: Field position salary: Salary in thousands (US dollars) a. Read in the dataset called 'mlbdata.csv' that is located on the website (in the Homework link) b. Create a histogram of the salary variable c. Describe the histogram d. Create a boxplot of salary by team (include main titles and axis labels) e. Estimate the true mean salary with 95% confidence Sampling populations of rectangles has recently become popular as a way to simulate estimation processes. A sample of n = 10 rectangles was drawn from a population of N = 1000 rectangles, giving areas of: 1, 4, 8, 10, 1, 6, 4, 12, 5, and 4. Estimate the mean mu of the population of rectangles, with 90%, 95%, and 98% confidence (all three (3) confidence levels). Use software to calculate these. A random sample of 50 lenses used in eyeglasses yields a sample mean of 3.05 mm and standard deviation of 0.34 mm. The specifications call for a desired thickness of 3.20 mm. Is there sufficient evidence that the true mean lense thickness is different than the specifications call for? a. List hypotheses b. Complete the test with software using the appropriate command (make sure you specify the mu and df)

Explanation / Answer

2)
n = 10 , mean = 5.5 , s = 3.59
mean of the population = 5.5

t value at 90% CI = 1.833
t value at 95% CI = 2.262
t value at 98% CI = 2.821

CI = mean +/- t * (s/sqrt(n))
= 5.5 +/- 1.833 * ( 3.59 / sqrt(10))
= (3.419 , 7.580)

CI = mean +/- t * (s/sqrt(n))
= 5.5 +/- 2.262 * ( 3.59 / sqrt(10))
= (2.932 , 8.067)

CI = mean +/- t * (s/sqrt(n))
= 5.5 +/- 2.821 * ( 3.59 / sqrt(10))
= (2.297 , 8.702)

3)
Hypothesis:
H0 : mu = 3.20
Ha : mu not equal to 3.20

Test statistic:

x = 3.05 , s = 0.34 , mean `= 3.20 , n =50

t = ( x -mean) /( s /sqrt(n))
= ( 3.05 - 3.20)/( 0.34 / sqrt(50))
= -3.119

p value is calculated using t = -3.119 ,df = 49
p value = .001518.

we reject the null hypothesis

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