A drug manufacturer is producing a medicine which is designed to reduce fevers. The company samples...

A drug manufacturer is producing a medicine which is designed to reduce fevers. The company samples it on 30 people who had an average temperature of 101.4°F. After taking the medicine the average body temperature fell to 99.6°F. There was a sample standard deviation of 1.2°F. The company will only produce and market the product if it is at least 95% confident that the product significantly lowers body temperature; a hypothesis test is undertaken to determine if the product will be marketed.

What is the null hypothesis?

What is the alternative hypothesis?

What are the degrees of freedom?

What is the critical t-value?

What is the test statistic for the sample?

What is the conclusion?

Solutions

Expert Solution

Null hypothesis H0: The average body temperature after taking the medicine is same as before taking the medicine which is 101.4°F.

Alternative hypothesis Ha: The average body temperature after taking the medicine is lower than before taking the medicine which is 101.4°F.

Degree of freedom = n-1 = 30-1 = 29

For 95% confidence level and left tail test, the critical t-value is -1.70

That is, we reject the null hypothesis when t < -1.70

Standard error of mean = s / = 1.2 / = 0.219089

Test statistic, t = ( - ) / Std error = (99.6 - 101.4) / 0.219089 = -8.22

Since the test statistic t is less than the critical value -1.70 and falls in the rejection region, we reject null hypothesis H0 and conclude that there is significant evidence that the average body temperature after taking the medicine is lower than 101.4°F.

orchestra answered 1 year ago

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