Body temperature is known to be distributed normally among healthy adults, with
ID: 3220123 • Letter: B
Question
Body temperature is known to be distributed normally among healthy adults, with an average body temperature of 98.6 degrees Fahrenheit among healthy adults in the US. You collect data from a random sample of 20 healthy adults in your community and find that your sample temperatures have a mean of 98.4 and a sample standard deviation of 0.3 (both in degrees Fahrenheit). You use the t-ratio to test the null hypothesis that body temperature among healthy adults in your community does not differ from the body temperature observed in the US population of healthy adults. You retain the null based on the computed t-value of 1.5. Write a sentence describing your results. Make sure to format your results sentence appropriately.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: = 98.6
Alternative hypothesis: 98.6
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
DF = n - 1 = 20 - 1
D.F = 19
t = (x - ) / SE
t = 1.5 (Given)
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the t statistic having 19 degrees of freedom is less than -1.5 or greater than 1.5.
We use the t Distribution Calculator to find P(t < -1.5) = 0.075, and P(t > 1.5) = 0.075
Thus, the P-value = 0.075 + 0.075 = 0.15
Interpret results. Since the P-value (0.15) is greater than the significance level (0.05), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that average body temperature for adults differs from 98.6 degrees Fahrenheit.