Question

Important instructions: For all situations requiring a hypothesis test (z test, one-sample t test, one-sample variance test or two-sample t test), you must 1. Choose the appropriate test based on the information you are given 2. State null and alternative hypotheses 3. Choose a one or two tailed test and explain why you chose that test 4. Calculate the appropriate test statistic, showing all work neatly. This includes calculations of means, standard deviations, etc. 5. Draw the appropriate conclusions (i.e., do you reject or fail to reject Ho?) To help you know for sure which questions require this, I have marked the questions requiring these steps with an asterisk (*). You may assume data are normal and have equal variances that necessary assumptions have been fulfilled.

Answer 1

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.