The manufacturer of an over-the-counter heartburn relief mediation claims that i

Question

The manufacturer of an over-the-counter heartburn relief mediation claims that it product brings relief in less than 3.5 minutes, on average. To be able to make this claim the manufacturer was required by the FDA to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 heartburn sufferers, the mean time to relief was 3.3 minutes and the population standard deviation was 1.1 minutes. Test the hypotheses at a significance level alpha = .05 using the critical value approach.

Explanation / Answer

Here the population standard deviation is known so we use z-test.

Null and Alternative Hypothesis:

H0: µ 3.5

H1: µ < 3.5

Level of significance = .05

Test Statistics:

Z = (x bar - µ) / (s/sqrt(n))                           [sqrt = square root ]

= (3.3 – 3.5)/(1.1/sqrt(50))

= -1.29

From the Normal Table we get the critical value as -1.645

Here our test statistics is greater than the critical value (-1.29 >-1.645); we fail to reject the null hypothesis.

There is not sufficient evidence to support the claims that it product brings relief in less than 3.5 minutes on average.

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