Question

7. Use tab 7. (Hospital charges) in DS3.xls and do the following:
   1. Calculate the mean and median of age, LOS and charges using the =AVERAGE() and =MEDIAN() functions. (3 points)
   2. Based on the results from ‘a.’ above, in which direction, if any, are each of these three distributions (age, LOS, charges) skewed? (4 points)
   3. Calculate the variance and standard deviation of age, LOS and charges using the =VAR.S() and =STDEV.S() functions. (3 points)
8. Write out the formula for calculating the 95% confidence interval for a sample mean. (5 points)
9. In this problem, you will compute confidence intervals for the mean under a variety of conditions and compare the results. You will also discuss what accounts for differences in these confidence intervals, if any. Please use Tab 9. In DS3.xlsx to show your work and report your results with two digits to the right of the decimal point.
   1. Using =T.INV.2T() and the formula for calculating the confidence interval, calculate the exact 95% confidence interval (upper and lower limits) for the following: (4 points)
      1. n = 40, mean = 32, S.D. = 6
      2. n = 40, mean = 32, S.D. = 12
      3. n = 140, mean = 32, S.D. = 6
      4. n = 140, mean = 32, S.D. = 12
   2. Using t = 2 and the formula for calculating the confidence interval, calculate the approximate 95% confidence interval (upper and lower limits) for the following: (2 points)
      1. n = 40, mean = 32, S.D. = 6
      2. n = 40, mean = 32, S.D. = 12
   3. Compare the confidence intervals computed in a.i and a.ii, above. What accounts for any differences observed. (1 point)
   4. Compare the confidence intervals computed in a.i and a.iii, above. What accounts for any differences observed. (1 point)
   5. Compare the confidence intervals computed in b.i and b.ii, above. What accounts for any differences observed. (1 point)
   6. Compare the confidence intervals computed in a.i and b.i, above. What accounts for any differences observed. (1 point)
10. In the next problem, you will compute confidence intervals for two means and use these to test hypotheses concerning these means. You will also compute the confidence interval for a proportion. Using the data in Tab 10. (Charges) in DS3.xlsx. Please report your results with two digits to the right of the decimal point. Assume that the data represent a random sample from a larger population and do the following:
    1. Calculate the exact 95% confidence interval (lower and upper limits) for the sample mean of LOS. (2 points)
    2. Use the confidence interval calculated in “a” above to test the hypothesis that the mean LOS is 5.5 days. (2 points)
    3. Calculate the exact 99% confidence interval (lower and upper limits) for the sample mean of charges. (2 points)
    4. Using the confidence interval calculated in “c” above, test the hypothesis (at the alpha = 1% level) that the mean of charges is $4,700. (2 points)
    5. Compute the 95% confidence interval for the proportion female. (Hint: You will need to calculate the proportion of records that are for females and the S.E. for this proportion). (2 points)

PLEASE USE DATA BELOW:

Sex   Age   LOS   Charges
F   75   3   $5,041.93
F   72   3   $4,318.13
F   56   1   $707.70
M   89   5   $5,399.67
F   49   2   $3,405.38
F   69   4   $2,384.47
F   85   2   $2,590.86
M   79   5   $7,000.21
M   70   1   $2,404.39
F   72   5   $5,029.09
F   80   5   $4,177.90
M   85   10   $8,244.25
M   90   6   $5,184.53
F   70   5   $17,480.97
M   86   5   $4,734.98
F   80   4   $3,026.42
F   83   7   $8,118.92
F   78   3   $17,005.45
F   80   12   $17,605.59
F   84   10   $18,290.04
F   83   6   $6,460.59
F   68   9   $10,955.29
M   88   4   $2,421.63
F   83   9   $10,421.01
F   73   6   $11,045.79
F   83   6   $5,482.93
F   73   5   $5,082.83
F   76   2   $3,004.67
F   72   5   $6,450.77
M   86   3   $4,637.96
M   69   2   $1,547.81
F   92   2   $1,905.65
F   82   1   $1,078.56
M   83   16   $10,655.80
M   46   4   $2,426.48
M   39   1   $1,596.91
F   89   2   $3,311.66
M   91   3   $3,078.99
F   76   2   $2,721.63
F   68   7   $5,547.71
F   80   1   $1,820.41
F   76   3   $4,242.10
F   88   5   $3,169.19
M   77   3   $3,620.78
F   75   2   $5,384.92
F   50   2   $2,581.72
F   82   3   $3,542.79
F   76   4   $2,489.65
F   84   6   $3,548.05
F   94   11   $8,953.38
M   76   3   $1,876.70
F   94   14   $19,708.11
M   88   3   $2,694.11
F   74   1   $1,599.82
M   73   1   $2,472.64
F   81   2   $5,019.86
M   66   6   $2,945.22
F   79   2   $2,834.68
M   83   3   $1,871.78
F   87   8   $6,815.61
F   82   11   $11,179.97
M   85   14   $10,242.50
F   83   5   $3,034.14
F   90   9   $7,022.47
F   77   7   $7,792.24
F   76   10   $14,769.92
F   94   6   $5,804.21
F   91   7   $6,823.60
M   49   9   $7,024.64
F   75   2   $2,146.99
M   91   7   $6,424.30
M   71   10   $12,919.48
F   71   7   $11,098.70
F   76   2   $4,860.83
F   77   7   $4,425.44
M   85   4   $5,151.52
M   75   7   $5,363.25
M   81   7   $5,216.91
M   78   2   $5,756.89
F   75   3   $5,621.92
M   76   3   $6,864.63
F   78   2   $3,489.88
F   70   10   $7,596.68
M   60   5   $6,572.60
F   67   2   $12,313.78
F   91   4   $3,720.09
M   96   11   $8,217.27
F   72   1   $1,035.75
F   90   4   $3,674.03
M   92   2   $2,451.69
F   82   10   $9,931.21
F   61   8   $8,954.81
M   76   3   $4,286.90
F   88   2   $1,731.73
F   65   6   $3,580.55
F   82   6   $5,330.24
M   78   10   $6,015.34
M   79   4   $4,655.83
M   73   2   $2,781.28
M   77   3   $4,713.26

Answer 1

First four questions have been answered

Calculate the mean and median of age, LOS and charges using the =AVERAGE() and =MEDIAN() functions. (3 points)

Calculate the variance and standard deviation of age, LOS and charges using the =VAR.S() and =STDEV.S() functions. (3 points)

Both done below

Based on the results from ‘a.’ above, in which direction, if any, are each of these three distributions (age, LOS, charges) skewed? (4 points)

Age : Mean is equal to median hence it is normal distributed.
LOS : Mean is greater than median hence it right skewed distribution
Charges : Mean is greater than median hence it right skewed distribution

Write out the formula for calculating the 95% confidence interval for a sample mean. (5 points)

In this problem, you will compute confidence intervals for the mean under a variety of conditions and compare the results. You will also discuss what accounts for differences in these confidence intervals, if any. Please use Tab 9. In DS3.xlsx to show your work and report your results with two digits to the right of the decimal point.
Using =T.INV.2T() and the formula for calculating the confidence interval, calculate the exact 95% confidence interval (upper and lower limits) for the following: (4 points)
n = 40, mean = 32, S.D. = 6
n = 40, mean = 32, S.D. = 12
n = 140, mean = 32, S.D. = 6
n = 140, mean = 32, S.D. = 12

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