Question

A cosmetic company is interested in testing the effectiveness of a new cream for treating skin blemishes. It measured the effectiveness of the new cream compared to the leading cream on the market and a placebo. Data below shows the number of blemishes removed after using the cream for 1 week. Assume two-tailed with an α = .05.

New Cream	Leading Cream	Placebo Cream
81	48	18
32	31	49
42	25	33
62	22	19
37	30	24
44	30	17
38	32	48
47	15	22
49	40	18
41	48	20

Write hypotheses

Determine the Critical value

Compute test statistic

evaluate the null

Answer 1

Null hypothesis : means of all three groups are same

Alternative hypothesis : at least one mean is different

Using Excel, (Data -> Data Analysis -> Anova: Single Factor), we get the following output -

Now,

The value of F statistic = 7.189

and P-value = 0.00314

Since P-value < 0.05, so we reject the null hypothesis and we can conclude that new cream is more effective than the leading cream on the market and a placebo.