Question

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

Population standard deviation is known and the sample is large, $\ge30$ , thus, normal distribution is used.

$H_o\mu=100$

$H_a\mu\ne100$

Assume 95% confidence level.

$CV, Z_{0.025}=1.96$

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

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

Since the calculated statistic 14.61 is grater than the critical value, 1.96, we reject the null hypothesis and conclude that the raw cornstarch had an effect on blood glucose level.