Answer the questions: Step 1 - state the null hypothesis and the alternative hyp

Question

Answer the questions:

Step 1 - state the null hypothesis and the alternative hypothesis

Step 2 - Select the level of significance

Step 3 - Evaluate the test statistic

Step 4 - Formulate a decision rule with critical value of test statistic

Step 5 - Compare the test statistic to the critical value and make the decision about H0

4.6

F-Test Two-sample for Variances Use Excel’s 2-sample variances data analysis tool to solve the following problem. A well-known ice cream store wants to test two different methods for scooping ice cream so they can use the one that has the least variability in their training of new and current employees. It took a sample of the ice cream cones scooped and measured the weights. Use the F-Test Two-Sample for Variances to test the hypothesis that the variances between the two methods are the same. Interpret the results. Method 1 Method 2 4.7 3.6 3.9 4.3 3.2 3.9 3.8 5.4 3.9 4.1 4.8 4.7 3.6 4.8 5.1 3.5 4.8 3.9 5.3 3.9 3.4 4.8 4.2 5 5.3 4.4

Answer the questions:

Step 1 - state the null hypothesis and the alternative hypothesis

Step 2 - Select the level of significance

Step 3 - Evaluate the test statistic

Step 4 - Formulate a decision rule with critical value of test statistic

Step 5 - Compare the test statistic to the critical value and make the decision about H0

4.6

Explanation / Answer

F-Test Two-sample for Variances:

1.Null hypothesis – H0 : 12 = 22
Alternative hypothesis – H1 : 12 > 22,
where 1 and 2 are the standard deviations of method 1 and method 2 values respectively.

2. Level of significance : = 0.05

3. Test Statistic:      F = s21 / s22, where s21 and s22 are the sample variances of method 1 and method 2 respectively.

4. Critical Region:   The hypothesis that the two variances are equal is rejected if,

F >F,N11,N21, where F, N1-1, N2-1 is the critical value of the F distribution with N1-1 and N2-1 degrees of freedom and a significance level of .

5.Here, N1 = 12, N2 = 15.

F-Test Two-Sample for Variances

Method 1

Method 2

Mean

4.225

4.413333

Variance

0.483864

0.351238

Observations

12

15

df

11

14

F

1.377594

P(F<=f) one-tail

0.282171

F Critical one-tail

2.565497

Here, since F < F Critical one-tail, we accept H0 and conclude that there is no significant difference between the variance of the two methods.

F-Test Two-Sample for Variances

Method 1

Method 2

Mean

4.225

4.413333

Variance

0.483864

0.351238

Observations

12

15

df

11

14

F

1.377594

P(F<=f) one-tail

0.282171

F Critical one-tail

2.565497

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