Could you please include the steps to the solution as well as use the critical v

Question

Could you please include the steps to the solution as well as use the critical value approach. Thank you

Question 7 Three different brands of pain relief medication are available for minor aches and pains. It is of interest to know whether the mean time to relieve the pain differs from brand to brand. To find out, twelve individuals with minor aches and pains were randomly assigned to one of the three brands. The time to relieve the pain (in minutes) for each individual is provided in the table below. Brand A Brand B Brand C 20 15 20 12 marks Given that the necessary assumptions are satisfied, can it be concluded, at the 2.5% level of significance, that not all mean times to relieve pain are equal? Formulate and test the appropriate hypotheses. Use the critical value approach.

Explanation / Answer

Here we need to compare more than three means. So one way ANOVA will be used.

Hypotheses are:

H0: All the populaton means are equal.

Ha: At least one population mean differs from other.

Following is the output of one way ANOVA analysis:

The p-value is 0.0799

Since p-value is greater than 0.025 so we fail to reject the null hypothesis. That is we cannot conclude that there is signifcant difference between the means.

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The critical value is 5.714

The test statistics is F = 3.389

Since F < 5.714 so we fail to reject the null hypothesis. That is we cannot conclude that there is signifcant difference between the means.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Brand A 4 51 12.75 4.916667 Brand B 4 81 20.25 18.25 Brand C 4 76 19 34 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 129.1667 2 64.58333 3.389213 0.079947 5.714705 Within Groups 171.5 9 19.05556 Total 300.6667 11

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