Question

A medical researcher believes that a drug changes the body's temperature. Seven test subjects are randomly selected and the body temperature of each is measured. The subjects are then given the drug, and after 30 minutes, the body temperature of each is measured again. The results are listed in the table below. Is there enough evidence to conclude that the drug changes the body's temperature? Let d=(body temperature after taking drug)−(body temperature before taking drug) d=(body temperature after taking drug)−(body temperature before taking drug) . Use a significance level of α=0.02 for the test. Assume that the body temperatures are normally distributed for the population of people both before and after taking the drug.

Temperature (before) 100.2 100.2 100.4 100.4 99.6 99.6 98.8 98.8 98.8 98.8 100.3 100.3 100.7 100.7

Temperature (after) 99.4 99.4 99.7 99.7 100.2 100.2 98.2 98.2 98.5 98.5 99.6 99.6 100.3 100.3

Step 3 of 5 : Compute the value of the test statistic. Round your answer to three decimal places.

Answer 1

There are 7 test subjects and hence the sample size is 7. Hence, there will be 7 temperature recordings before administering the drug and 7 of them after. (Assuming that each temperature has been repeated twice to give 14 recordings and considering them only once to get the clean data. In either case you will be able to solve it even if the data is different by following the methodology below).

Since, the same subject is tested twice, this is a paired sample, and we will do a paired-sample t-test for a difference in means.

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To compute test statistic, first fill in the values in excel or any software of your choosing. You can do it by hand as well.

Then calculate 'd' which is difference in the body temperatures after and before taking the drug which is specified in the question as well.

Resulting data:

Then calculate the sample mean and sample standard deviation of the d-values.

You can do this by using the functions AVERAGE(C2:C8) and STDEV.S(C2:C8) in Excel.

You can also calculate by hand using the general formulas for mean and standard deviation.

Result:

For this particular test, Test- statistic or t-test statistic is given by the formula:

where, = Sample mean of the differences which is already calculated.

= Sample standard deviation which is also calculated already.

n = sample size = 7

= Hypothesized mean difference which is 0 as we are conducting a difference in means test to see if the drug is effective or not.

So, substituting these values into the equation, we have:

--> t = -2.278 (Rounded to three decimal places)

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Thanks. Please let me know in case of any additional clarifications needed through comments.

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