Question

3.    An appliance manufacturing company want to test microwave ovens being sold. The researcher has identified three different types based on the number of watts of the ovens. Three random samples are taken and the data is given below:

                                            Watts

                800 900 1000

                180                         235                         225

                175                         135                         225

                200                         160                         190

                170                         230                         215

                190                         250                         250

                180                         200                         230

                185                         200                         170

                160                         210                         179

                195                         199                         200

a) Create a table of group sample means and sample standard deviations.

b) Create an appropriate graph. Copy and paste the graph into your Word document. Do the means appear to be equal based on your graph?

c) Carry out the ANOVA. Report the F statistic, its p-value and state your conclusion. Copy and paste the results of the ANOVA test into your Word document.

Answer 1

a)

b)

Yes, from the given below boxplot of the samples taken we can conclude that the mean is different for the three types of microwaves.

c)

Null and Alternative Hypothesis:

H₀: All Means are equal

H₁: Not all Means are equal

Alpha = 0.05

N = 27

n = 9

Degress of Freedom:

df_Between = a – 1 = 3-1 =2

df_Within = N-a = 27-3 = 24

df_Total = N-1 = 27-1 = 26

Critical Values:

Time (df_Between, df_Within) : (2,24) = 3.40

Decision Rule:

If F is greater than 3.40, reject the null hypothesis

Test Statistics:

SS_Betwen = ?(?a_i)²/n - T²/N = 3706.74

SS_Within = ?(Y)² - ?(?a_i)²/n = 17292.89

SS_Total = SS_{Betwen ­­}+ SS_Within = 20999.63

MS = SS/df   

F = MS_effect / MS_error

Hence,

F = 1853.37/ 720.54 = 2.57

P-value = 0.0972

Result:

Our F = 2.57, we fail to reject the null hypothesis

Conclusion:

All means are equal.