3. A nutritionist in a large company’s cafeteria has a guideline saying employee

Question

3. A nutritionist in a large company’s cafeteria has a guideline saying employees’ daily zinc intake should be about 14 mg/day. She selects a simple random sample of 70 employees and measures their zinc intake for one day. She finds their average intake is 13.8 mg. Earlier studies suggest that the population standard deviation of intakes is about 0.9 mg. (a) Run a test, using significance level = 0.05, to decide whether these data are stong evidence that the whole company population of employees took in too little zinc that day. • Hypotheses: • Assumptions: • Test statistic: • p-value: • Conclusion: (b) Suppose the population mean really was 14. Before sampling, what was the probability the test would reject H0 : µ = 14 even though it is true? Which type of error is this?

Explanation / Answer

Solution:

a) Test hypothesis:
H0: = 14
Ha: < 14
Assume normally distributed and sample is selected independently.
Test statistics Z = x - / /n
= (13.8-14) /(0.9/70)
= -1.86
P-value = 0.0314 by using z-score table

b) Since p-value = 0.0314 < = 0.05, So we have enough evidence against null hypothesis. Reject null hypothesis even though it is true. This is called Type II error

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