You want to compare the efficiency of workers in your manufa

You want to compare the efficiency of workers in your manufacturing company, i.e.,
between the day shift and the swing shift. You obtained the weekly average of
products they completed during the first quarter of this year as shown below. Is
there a significant difference in worker efficiency between the two shifts? Using the
five steps of hypothesis testing, test at .05, twotailed test. (Hint: Use the
computational formula for SS.)
Day Shift Swing Shift
10 9
12 10
8 12
9 8
11 7
13 11
12 8
10 10

Solution

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 mu2

where mu1 and mu2 are population differences.

Before that we have to test the hypothsis that ,

H0 : variances are equal.

H1 : variances are not equal.

alpha = level of significance = 0.05

The test statistic is,

F = larger variance / smaller variance

We have to use the formula for variance is,

variance (SS) for day shift(SSx1) = X1² - (X1)² / n1

where X1 = Day shift

X2 = Swing shift

n1 = number of observations for day shift = 8

n2 = number of observations for swing shift = 8

variance (SS) for day shift(SSx2) = X2² - (X2)² / n2

We can calculate equality of variances using TI-83 calculator.

steps :

START --> EDIT --> ENTER --> Enter data in L1 and L2 --> STAT --> TESTS --> D : 2-SampFTest --> ENTER --> Inpt : Data --> List1 : L1 --> List2 : L2 --> Freq1 : 1 --> Freq2 : 2 --> select first option --> calculate

Output :

F = 1

P = 0.9999

SSx1 = 1.6850

SSx2 = 1.6850

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : Variances are equal.

Here we use pooled variance.

Now we are testing two means by using TI-83 calculator.

Steps :

STAT --> TESTS --> 4: 2-SampTTest --> ENTER -->  --> Inpt : Data --> List1 : L1 --> List2 : L2 --> Freq1 : 1 --> Freq2 : 2 --> select first option --> Pooled variance : Yes --> calculate

Output is,

t = 1.4837

P-value = 0.1601

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : There is not significant difference in worker efficiency between the two shifts.