Question

We work for Cola Company and there have been some discussions on which pressure setting is best for filling out bottles. If we overfill the bottles then we are spending money we do not need to. If we are under filling the bottles we run the risk of dissatisfaction of the customers. If we can fill the bottles using a higher psi we can run the line faster and thus increase our production. Our current fill pressure is 25psi. Management wants to know if there is a different variation from the standard between the two pressure settings.

ml (25psi volume): 1007.2, 1008.4, 1010.2, 1011.2, 1008.0, 1009.0, 1011.4, 1013.4, 1010.6, 1010.9

ml (30psi volume): 1001.2, 1003.1, 1003.6, 1001.4, 1002.7, 1004.3, 1002.6, 1005.0, 1003.7, 1004.4

Sample size of first set =

Sample size of second set =

Sample mean of first set =

Sample mean of second set =

Sample standard deviation of the first set =

Sample standard deviation of the second set =

Estimate of variance =

Confidence Coefficient =

Alpha =

Calculated Degrees of Freedom =

Calculated Test Statistic =

What can you conclude by observing your confidence limits? (No difference or there is a difference?) =

Answer 1

Solution:-

Sample size of first set = 10

Sample size of second set = 10

Sample mean of first set = 1010.03

Sample mean of second set = 1003.2

Sample standard deviation of the first set = 1.87264

Sample standard deviation of the second set = 1.25433

Confidence Coefficient = 95%

Alpha = 0.05

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H₀: σ_A² = σ_B²

Alternative hypothesis H_A: σ_A² σ_B²

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (F).

DF₁ = n₁ - 1 = 10 -1

D.F₁ = 9

DF₂ = n₂ - 1 = 10 -1

D.F₂ = 9

Test statistics:-

F = 2.23

Since the first sample had the smaller standard deviation, this is a right-tailed test.

p value for the F distribution = 0.124 .

Interpret results. Since the P-value (0.124) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test there is insufficient evidence to conclude that there is difference in variance.