Question

10. Poverty and Calcium Calcium is the most abundant mineral in the body and also one of the most important. The recommended daily allowance (RDA) of calcium for adults is 800 milligrams (mg). A random sample of 18 people with incomes below the poverty level gives the following daily calcium intakes: 686, 433, 743, 647, 734, 641, 993, 620, 574, 634, 850, 858, 992, 775, 1113, 672, 879, 609

At the 1% significance level, do the data provides sufficient evidence to conclude that the mean calcium intake of all people with income levels below the poverty level is less than the RDA of 800 mg?

Step 1

Step 2

Step 3-Critical value approach

Step 4-Conclusion

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 800
Alternative Hypothesis, Ha: μ < 800

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (751 - 800)/(176.5779/sqrt(17))
t = -1.144

Rejection Region
This is left tailed test, for α = 0.01 and df = 16
Critical value of t is -2.583.
Hence reject H0 if t < -2.583

fail to reject null hypothesis.
There is not sufficient evidence to conclude that the mean calcium intake of all people with income levels below the poverty level is less than the RDA of 800 mg