1. What is the 95% CI for the difference between the mean starting salaries of t
ID: 3073202 • Letter: 1
Question
1. What is the 95% CI for the difference between the mean starting salaries of those who stay at least three years and those who leave before 3 years? Can you say that you are 95% sure there is a difference?
Case Study: Employee Retention at D&Y Employee Starting Salary On Road Pct State Univ CIS Degree Stayed 3 Years Tenure 1 38900 57% Yes Yes No 11 2 42300 68% Yes Yes No 5 3 39800 75% No Yes No 21 4 35700 29% No Yes Yes 5 40400 71% No Yes No 19 6 36400 62% No Yes No 18 7 37300 41% Yes No Yes 8 36600 37% No Yes No 17 9 34600 65% No Yes No 20 10 42300 53% Yes Yes No 16 11 37800 73% No Yes Yes 12 39700 60% No Yes No 12 13 36100 56% Yes Yes Yes 14 36100 42% Yes Yes Yes 15 33800 35% No Yes Yes 16 38900 36% No Yes Yes 17 35500 50% No Yes No 15 18 37600 58% No Yes Yes 19 38100 78% Yes Yes Yes 20 38300 16% No No Yes 21 34600 29% No Yes Yes 22 36300 26% No Yes Yes 23 37200 59% Yes Yes No 14 24 37700 55% Yes Yes Yes 25 36600 45% No Yes No 13 26 41000 81% Yes Yes No 9 27 40800 111% Yes Yes No 7 28 36700 56% Yes Yes Yes 29 37700 56% No Yes No 22 30 37700 42% No Yes No 11 31 39300 69% Yes Yes No 16 32 37500 50% No Yes No 18 33 40000 69% Yes Yes No 9 34 41500 64% Yes No No 5 35 39600 72% No Yes No 18 36 36900 42% No Yes Yes 37 39500 62% No Yes No 5 38 37800 20% No Yes No 23 39 38600 57% No Yes No 8 40 40600 70% Yes Yes Yes 41 41600 63% Yes Yes Yes 42 40800 44% No No Yes 43 36200 68% No Yes No 31 44 39600 59% No Yes No 10 45 36100 56% Yes Yes Yes 46 36100 42% No Yes Yes 47 39500 53% Yes Yes No 17 48 39100 38% No Yes Yes 49 40300 53% Yes Yes Yes 50 38800 78% Yes Yes Yes 51 39400 34% Yes Yes No 27 52 38400 23% No Yes Yes 53 35200 33% No Yes Yes 54 36100 24% No No Yes 55 37100 44% No Yes Yes 56 37200 64% Yes Yes No 23 57 36800 46% Yes No Yes 58 36500 27% No No Yes 59 35900 29% No No Yes 60 37900 76% Yes Yes No 14 61 37900 58% No Yes No 26 62 37900 28% No Yes No 14 63 36700 37% No Yes Yes 64 37400 49% No Yes No 19 65 38200 62% Yes Yes Yes 66 36600 51% Yes Yes No 7Explanation / Answer
We use minitab to solve this question-
We first test is the variance equal for salaries of Leave before 3 years and Stay at least three years.
Ho : S12 = S22 Vs Ha : S12 S22
The test statistics is,
F = S12 / S22 , S12 - Larger sample variance betwwen Leave before 3 years and
Stay at least three years and
S22 - smaller sample variance between Leave before 3 years
and Stay at least three years .
= 3600471 / 2968129
F =1.213044
P-value = P( F < 1.213044) = 0.2926
P-value > 0.05 , Do not reject Ho
Therefore we use pooled variance.
We use t test with pooled standard deviation as the variances of the salaries of Leave before 3 years and Stay at least three years are equal.
Minitab output-
MTB > TwoSample 'Leave before 3 years' 'Stay at least three years';
SUBC> Confidence 95.0;
SUBC> Test 0.0;
SUBC> Alternative 0;
SUBC> Pooled.
Two-Sample T-Test and CI: Leave before 3 years, Stay at least three years
Two-sample T for Leave before 3 years vs Stay at least three years
N Mean StDev SE Mean
Leave before 3 years 35 38620 1897 321
Stay at least three year 31 37271 1723 309
Difference = (Leave before 3 years) - (Stay at least three years)
Estimate for difference: 1349
95% CI for difference: (453, 2245)
T-Test of difference = 0 (vs ): T-Value = 3.01 P-Value = 0.004 DF = 64
Both use Pooled StDev = 1817.7075
___________________________________________________________________________
95% CI for the difference between the mean starting salaries of those who stay at least three years and those who leave before 3 years is (453, 2245).
From given sample information there is 95 % chance that difference lies in (453, 2245).
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