Question

Statistics (II) Final Name 2. (8%) We want to see if the workers on the day and night shifts differ significantly in their productivity levels. A sample of workers output from both shifts was taken. Test the null hypothesis at the 5% level of significance by using (a) a parametric test (b) a nonparametric test. 6/19/2019 Student ID Night Shift Day Shift 31 31 25 29 32 26 34 30 27 33 37 39 24 35 39 28 38 44 42 36 40

Answer 1

(a) Parametric test Let uD output from Day Shift output from night shift true mean true mean N Null hypothesis, Ho D HN Alternative hypothesis, Hi HD HN Before test the null hypothesis, we need to check the two population variances equal or not. Here we mention that we assume the two sets of observations come normal populations. Us. efrom two independent

Probability Plot of Day shift, Night shift Normal 95% CI 10 20 40 50 Day shift Night shift Day shift 99 99 Mean 33.5 StDev 6.671 N 10 95 95 AD 0.163 90 90 P-Value 0.918 Night shift 80 80 Mean 33.18 70 70 StDev 5.135 60 60 N 11 50 50 AD 0.272 40 40 P-Value 0.595 30 30 20 20 10 10 5 1 20 60 30 40 Percent

From the above plot we observe that the normality assumption holds.

Test and CI for Two Variances: Day shift, Night shift

Method

Null hypothesis Sigma(Day shift) / Sigma(Night shift) = 1
Alternative hypothesis Sigma(Day shift) / Sigma(Night shift) not = 1
Significance level Alpha = 0.05

Statistics

Variable N StDev Variance
Day shift 10 6.671 44.500
Night shift 11 5.135 26.364

Ratio of standard deviations = 1.299
Ratio of variances = 1.688

Test
Method DF1 DF2 Statistic P-Value
F Test (normal) 9 10 1.69 0.426
Since p-value>0.05 so we can assume the two population variances are same.

Two-Sample T-Test and CI: Day shift, Night shift

Two-sample T for Day shift vs Night shift

N Mean StDev SE Mean
Day shift 10 33.50 6.67 2.1
Night shift 11 33.18 5.13 1.5

Difference = mu (Day shift) - mu (Night shift)
Estimate for difference: 0.32
95% CI for difference: (-5.09, 5.72)
T-Test of difference = 0 (vs not =): T-Value = 0.12 P-Value = 0.903 DF = 19
Both use Pooled StDev = 5.9122

Since p-value>0.05 so we fail to reject null hypothesis and conclude that there is insufficient evidence to conclude that the workers on the day and night shifts differ significantly in their productivity levels.

(b)

Non parametric test:

Mann-Whitney Test and CI: Day shift, Night shift

N Median
Day shift 10 33.000
Night shift 11 33.000

Point estimate for ETA1-ETA2 is 0.500
95.5 Percent CI for ETA1-ETA2 is (-5.997,5.997)
W = 111.0
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.9719
The test is significant at 0.9719 (adjusted for ties)

Since p-value>0.05 so we fail to reject null hypothesis and conclude that there is insufficient evidence to conclude that the workers on the day and night shifts differ significantly in their productivity levels.