When testing for a difference between the means of a treatment group and a place

Question

When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained. Using a 0.05 significance level, is there sufficient evidence to support the claim that the treatment group (variable 1) comes from a population with a mean that is less than the mean for the placebo population? Explain. t-Test: Two Sample for Means Variable 1 Variable 2 65.10738 66.18251 31414 2 Mean 8102938 10.27387 Known Variance Observations 50 5 Hypothesized Mean Difference 0 one-tail T Critical one-tail 9 PCT

Explanation / Answer

From output:

Test statistics:

t = -1.773

Test is one tail.

So rejection region

If t <-1.644853, reject H0

Since test statistics is less than critical value so we reject the null hypothesis.

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P-value approach:

P-value is 0.0384

Since p-value is less than 0.05 so we reject the null hypothesis.

That is at 0.05 level of significance we can conclude that the treatment group comes from a population with a mean that is less than the mean for the palcebo population.

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