Question

According to the Mayo Clinic, a fasting blood sugar of 100 mg/dL is considered to be normal. A doctor claims that his patients have a lower fasting sugar due to a new drug that he prescribes. The data is shown to the left. Test the doctor's claim at 0.05 level of significance. Is the drug working? What might be some issues with this dataset?

Sample		Population
Mean	77.98571429	Mean	100
Std Dev	12.28465858
N	70			H0:	μ= 100
DF	69			Ha:	μ< 100	claim
				Reject null
Numerator	-22.0142857
Denominator	1.468297539
T- Score	-14.9930686
P- Value	1.06928E-23
Critical Value	-1.66723855
Significance	0.05

Answer 1

Since p-value = 1.06928E-23 < 0.05 i.e. H₀ can be rejected and hence we can say that there is enough evidence to conclude that doctor's patients have a lower fasting sugar due to a new drug that he prescribed and hence drug is working.

Some problems may be:

• Patients may not fasted the night before and hence less fasting sugar is due to the other reason and not drug.
• It may so happen that the patients so chosen already have less sugar and hence no contribution of the drug.

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