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Important instructions: For all situations requiring a hypothesis test (z test, one-sample t test, one-sample variance test o
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3)

Before After Difference(d)
12.6 12.5 0.1
12.2 12.3 -0.1
10.8 10.9 -0.1
10.9 10.7 0.2
11.6 11.7 -0.1
11.7 11.8 -0.1
11.9 11.9 0
12.5 13.1 -0.6
12.7 12.8 -0.1
13.3 13.4 -0.1
12.1 11.8 0.3
13.2 13.1 0.1
Total -0.5

We have given data before and after type that is dependent data so we use paired t-test.

Claim: There is a difference between the milk output after and the milk output before significantly greater than 0.

The null and alternative hypothesis is

HO : μα = 0

Hi: pd > 0

Our hypothesis is a one-tailed test because the alternative hypothesis has less than sign.

Level of significance = 0.05

Sample size = n = 12

Sample mean of difference = \bar{d} = - 0.0417

Sample standard deviation of difference = s_{d} = 0.2234

Test statistic is

t = Sd/ n

t= -0.0417 0.2234/12

Degrees of freedom = n - 1 = 12 - 1 = 11

Critical value = 1.796   ( Using t table)

Test statistic | t | < critical value we fail reject null hypothesis.

Conclusion:

There is NO difference between the milk output after and the milk output before significantly greater than 0.

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