Answer to Question #288007 in Statistics and Probability for Kate

Question

According to a dietary study, a high sodium intake may be related to ulcers, stomach cancer, and migraine

headaches. The human requirement for salt is only 220 milligrams per day, which is surpassed in most single

servings of ready-to-eat cereals. If a random sample of 15 similar servings of certain cereal has a mean sodium

content of 244 milligrams and a standard deviation of 24.5 milligrams, does this suggest at the 0.05 level of

significance that the average sodium content for a single serving of such cereal is greater than 220 milligrams?

Answer 1

$H_0: \mu = 220 \\ H_1: \mu > 220 \\ \bar{x} = 244 \\ s = 24.5 \\ n=20 \\ α=0.05 \\ df = n-1 = 20 -1=19$

Test-statistic

$t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \\ t = \frac{244-220}{24.5 / \sqrt{20}} = 4.381 \\ t_{crit} = t_{0.05,19} = 1.729$

Reject H₀ if test statistic t>1.729.

Since $t>t_{crit}$ , we reject the null hypothesis. We have sufficient evidence to conclude, that $\mu$ is greater than 220 at 5% significance level.