Sixty people were selected at random from a homogeneous population and divided i

Question

Sixty people were selected at random from a homogeneous population and divided into five groups. Each group was treated with a different medicine, and the time (in minutes) for the medicine to take effect on each person in each group was recorded in the following table in the columns marked X_1, X_2, X_3, X_4 and X_5. Do an ANOVA test at alpha (alpha) level of significance of 1% to determine if there is a significant difference among the mean response times of the five treatments. Calculate: a. Totals for all five groups, b. Means for all five groups, c. Grand mean, d. Sum of squared deviations among (SSA), e. Mean squared deviations among (MSA), f. Sum of squared deviations within (SSW), g. Mean squared deviations within (MSW), h. Degrees of freedom for numerator, i. Degrees of freedom for denominator, j. F-sample statistic, k. F-critical value at (use alpha = 01), l. State the null hypothesis (H_0), m. State the alternative hypothesis (H_1), n. What is the final conclusion?

Explanation / Answer

There are five groups.

Here we have to test the hypothesis that,

H0 : All means are equal.

H1 : Atleast one of the mean is differ than 0.

Assume alpha = level of significance = 1% = 0.01

Here we have to test more than two means so we use one way ANOVA.

We can do one way ANOVA in EXCEL.

steps :

ENTER data into EXCEL sheet --> Data --> Data ANalysis --> Anova : Single factor --> ok --> Input Range : Select all the data range --> Grouped by : Columns --> Click on labels in first row --> Alpha : 0.01 --> Output Range : select one empty cell --> ok

Output :

SSA = 178.6807

MSA = 44.0718

SSW = 615.3193

MSW = 11.18762

Numerator degrees of freedom = 4

Denominator degrees of freedom = 55

F samle statistic = 3.9928

F critical value = 2.540

Here F sample statistic > F critical value

Reject H0 at 0.01 level of significance.

Conclusion : Aleast one of the mean is differ than 0.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance X1 12 237 19.75 6.204545 X2 11 186 16.90909 6.490909 X3 12 214 17.83333 5.969697 X4 14 276 19.71429 18.21978 X5 11 167 15.18182 17.96364 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 178.6807 4 44.67018 3.992822 0.006484 2.539689 Within Groups 615.3193 55 11.18762 Total 794 59

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