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Boxplots, regression analysis, and sampling distributions

Please see attachment for fully formatted questions.
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1) The age of the 36 millionaires sampled are arranged in increasing order in the tables below.
Use the Descriptive statistics output and the graphs to answer the following questions:
a) Describe the distribution: Hint: Shape, Center, Spread and the outliers.
be sure to interpret your answers.
b) Does your histogram support your boxplot? Explain.
c) State the five number summary and interpret.

Millionaires
31 48 60 69
38 48 61 71
39 52 64 71
39 52 64 74
42 53 66 75
42 54 66 77
45 55 67 79
47 57 68 79
48 59 68 79

Descriptive Statistics

Variable N Mean Median StDev SE Mean
AGE 36 58.53 59.50 13.36 2.23

Variable Minimum Maximum Q1 Q3
AGE 31.00 79.00 48.00 68.75

2) An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least square method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volumes and total cost data for a manufacturing operation.

Production X Total Cost
400 4000
450 5000
550 5400
600 5900
700 6400
750 7000
450 4600
420 4600
370 3900
650 6300
650 6500
610 6200
720 7300
550 5000
600 6500
800 8000
850 8200
800 8500

Use the available output and graphs below to answer the following questions:

a) Explain the form, the direction and the strength of the relation ship between production and Cost.
b) State the estimated regression equation
c) Provide an interpretation for the slope of the estimated regression equation.
d) If the company's total cost next month is projected to be $7720, what will the production volume be?
e) What is the coefficient of determination r2? What percentage of the variation in total cost can be explained by production volume?
f) What is correlation coefficient r, does this number support your guess in (a)? Explain.
g) Did the estimated regression equation provide a good fit? Explain. Hint: r2
h) Does the residual plot support your answer in (g)? Explain.

The regression equation is

Predictor Coef StDev T P
Constant 475.2 341.1 1.39 0.183
Producti 9.2258 0.5473 16.86 0.000

S = 332.4 R-Sq = 94.7% R-Sq(adj) = 94.3%

3) Sampling distributions:
An automatic grinding machine in an auto parts plant prepares axles with a target diameter μ=40.135millimeters (mm). The machine has some variability, so the standard deviation of the diameter is σ= 0.003 mm. A sample of 4 axles is inspected each hour for process control purposes, and records are kept of the sample mean diameter. If the process mean is exactly equal to the target value, what will be the mean and standard deviation of the numbers recorded?

4) Confidence Interval:
You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $1400. Assume that the standard deviation is 220. Find a 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community. Interpret.

5) Cell phone bill
The following are the last year's local monthly bills, in dollars, for a random sample of 60 cell phone users. At 5% significance level, do the data provide sufficient evidence to conclude that last year's mean local monthly bill for cell phone users has decreased from the 1996 mean of $5025? Assume that σ = $25.
Hint: State your hypothesis, significant level α = 0.05, draw conclusion comparing p-value to α = 0.05
Use the output below to answer the questions. Don't forget to interpret and give recommendation(s)

Cell Phone Monthly Bills
25.07 42.13 16.74 16.50 24.86 35.38
77.54 15.83 29.13 45.00 23.78 32.09
33.21 32.81 42.37 35.97 31.93 40.66
31.42 13.85 17.26 20.28 48.65 12.90
16.46 15.70 61.64 29.28 65.01 12.65
104.53 30.42 45.15 46.87 50.81 18.18
47.98 14.95 15.45 28.41 46.57 46.37
62.30 51.95 58.00 16.89 81.49 29.00
44.07 127.17 13.81 49.68 28.37 43.23
117.29 27.43 22.76 89.28 35.93 100.80

Z-Test

Test of mu = 50.25 vs mu not = 50.25
The assumed sigma = 25.0

Variable N Mean StDev SE Mean Z P
BILL 60 40.69 26.25 3.23 -2.96 0.0031

Attachments

Solution Preview

Please see the attachment for fully formatted explanation.
======================================

1) The age of the 36 millionaires sampled are arranged in increasing order in the tables below.
Use the Descriptive statistics output and the graphs to answer the following questions:
a) Describe the distribution: Hint: Shape, Center, Spread and the outliers. be sure to interpret your answers.
The histogram and box plot suggest that the variable is symmetric about the mean. We can see that the first and third quartiles are equi distant from the median. The spread of the variable is determined by variance .

b) Does your histogram support your boxplot? Explain.
Yes . The histogram suggests that the data is approximately normally distributed. The formal test for normality (Anderson Darling) test also support this argument. Also the box plot suggests that symmetric

c) State the five number summary and interpret.
The five number summaray (Min, Q1, Median, Q3 and Max) are given below

Descriptive Statistics: Millionaires

Variable N* Minimum Q1 Median Q3 Maximum
Millionaires 0 31.00 48.00 59.50 68.75 79.00

Millionaires
31 48 60 69
38 48 61 71
39 52 64 71
39 52 64 74
42 53 66 75
42 54 66 77
45 55 67 79
47 57 68 79
48 59 68 79

Descriptive Statistics

Variable N Mean Median StDev SE Mean
AGE 36 58.53 59.50 13.36 2.23

Variable Minimum Maximum Q1 Q3
AGE 31.00 79.00 48.00 68.75

2) An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least square method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing ...

Solution Summary

The solution provides step by step method for the calculation of regression equations, Boxplots, , sampling distributions, confidence intervals, and hypothesis testing. Formula for the calculation and Interpretations of the results are also included.

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