Answer to Question #131603 in Statistics and Probability for Keagan

Question

1.3.Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 15. A
researcher thinks that a diet high in raw cornstarch will have a positive or negative effect on blood
glucose levels. A Sample of 30 patients who have tried the raw cornstarch diet has a mean glucose
level of 140.
Test the hypothesis that the raw cornstarch had an effect.

Answer 1

Since the population standard deviation is known, Z-test is used.

$H_0:\mu=100$

$H_1:\mu\ne100$

Let $\alpha=0.05$

$Z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}$

$Z_{0.05}=1.96$ (two tailed)

$Z=\frac{140-100}{\frac{15}{\sqrt{30}}}=14.61$

Since $Z=14.61>1.96$ , we reject the null hypothesis and conclude that the raw cornstart had an effect at 5% level of significance.