The mean BMI in patients free of diabetes has been reported

The mean BMI in patients free of diabetes has been reported as 28.2. An investigator measured BMI in 12 patients who are free of diabetes and found a mean BMI of 31.7 with a standard deviation of 5.9. The investigator hypothesizes that the BMI in patients free of diabetes is higher than what has been reported. Is there evidence that the BMI is significantly higher that 28.2? Use a 5% level of significance. You must report the null and alternative hypotheses, calculate the test statistic (show your work), and give the conclusion including a comparison to alpha or the critical value

Solution

mu for BMI in diabetes patients =28.2

x bar = 31.7 andn = 12

std error = s/rt 12 = 1.7032

Hypotheses:

H0: x bar = mu

Ha: x bar < mu

t statistic = (31.7-28.2)/1.7032

= 2.055

df = 12-1 = 11

Alpha = 5%

The P-Value is .032209.

The result is significant at p < .05.

Hence it is evident that BMI is significantly higher that 28.2? Use a 5% level of significance