According to “Dietary Goals for the United States (1997)”, high sodium intake may be related to ulcers, stomach cancer, and migraine headaches. The human requirement for salt is only 220 milligram per day, which is surpassed in most single servings of ready-to-eat cereals. If a random sample of 20 similar servings of Special K has a mean sodium content of 244 milligrams and a standard deviation 24,5 milligrams does this suggest at 0,01 level of significance that the average sodium content for single servings of Special K is greater than 220 milligrams? Assume the distribution of sodium content to be normal. The value of the test statistic for testing this hypothesis is ____

Answer 1

To test whether the average sodium content for single servings of Special K is greater than 220 milligrams, we can use a one-sample t-test.

The null hypothesis (H0) is that the average sodium content is equal to or less than 220 milligrams.
The alternative hypothesis (Ha) is that the average sodium content is greater than 220 milligrams.

The test statistic can be calculated using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Let's calculate the test statistic:
Sample mean = 244 milligrams
Hypothesized mean = 220 milligrams
Standard deviation = 24.5 milligrams
Sample size (n) = 20

t = (244 - 220) / (24.5 / sqrt(20))
t ≈ 5.2

To find the critical value for a 0.01 level of significance, we need to use a t-distribution table with degrees of freedom equal to (n-1) = (20-1) = 19.

Looking up the critical value for a one-tailed test with 0.01 level of significance and 19 degrees of freedom, we find the critical value to be approximately 2.861.

Since the test statistic (t = 5.2) is greater than the critical value (2.861), we reject the null hypothesis. This suggests that at a significance level of 0.01, the average sodium content for single servings of Special K is significantly greater than 220 milligrams.