The manufacturer of an over-the-counter heartburn relief mediation claims that its 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 standard deviation was 1.1 minutes.Calculate the appropriate test statistic to test the hypotheses.

Question

Quizplus · Accepted Answer

We need to conduct a one-sample t-test since we only have one sample to compare to the population mean of 3.5. The formula for the t-test is (sample mean - population mean) / (sample standard deviation / square root of sample size).

Plugging in the values, we get: 
(3.3 - 3.5) / (1.1 / sqrt(50)) = -1.29

The t-value is negative because the sample mean is less than the population mean. Comparing this t-value to a t-distribution with 49 degrees of freedom (50 - 1), using a two-tailed test at a significance level of 0.05, we find the critical t-value to be ±2.01. Since the calculated t-value of -1.29 falls within the acceptance region, we fail to reject the null hypothesis that the mean relief time is equal to or greater than 3.5 minutes. Therefore, the manufacturer's claim cannot be supported by this sample data.

The Manufacturer of an Over-The-Counter Heartburn Relief Mediation Claims That