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 X1, X2, X3, X4 and X5. Do an ANOVA test at alpha () level of significance of 1% to determine if there is a significant difference among the mean response times of the five treatments.

Using Excel 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 = .01),

l. State the null hypothesis (H0),

m. State the alternative hypothesis (H1),

n. What is the final conclusion?

X1: 19, 15, 24, 23, 22, 21, 20, 19, 18,18, 20, 18

X2: 16, 12, 21, 20, 19, 18, 17, 16, 15, 15, 17

X3: 17, 13, 22, 21, 20, 19, 18, 17, 16, 16, 18, 17

X4: 15, 21, 20, 24, 22, 14, 18, 18, 17, 17, 19, 28, 27, 16

X5: 11, 17, 16, 20, 18, 10, 14, 10, 11, 22, 18

Explanation / Answer

since p-value = 0.0064 < 0.01

we rejct the null hypothesis

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Row 1 12 237 19.75 6.204545 Row 2 11 186 16.90909091 6.490909 Row 3 12 214 17.83333333 5.969697 Row 4 14 276 19.71428571 18.21978 Row 5 11 167 15.18181818 17.96364 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 178.6807359 4 44.67018398 3.992822 0.006483992 2.539688635 Within Groups 615.3192641 55 11.18762298 Total 794 59

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