Question

Question 1

Select one answer.

In the article "Foods, Fortificants, and Supplements: Where Do Americans Get Their Nutrients?" researchers analyze the nutrient and vitamin intake from a random sample of 16,110 U.S. residents. Researchers compare the level of daily vitamin intake for vitamin A, vitamin B-6, vitamin B-12, vitamin C, vitamin D, vitamin E and calcium. Unless otherwise stated, all hypothesis tests in the study are conducted at the 5% significance level.

Researchers conduct a hypothesis test to determine if the proportion of U.S. residents consuming recommended levels of calcium is different among women and men. The p-value is 0.035, and researchers conduct this test at a 5% level of significance. What does a p-value of 0.035 mean?

1. There is a 3.5% chance that there is no difference in calcium consumption for women and men.
2. If the calcium consumption rates are different for the women and men, there is a 3.5% chance that future experiments will show the same difference in calcium consumption as observed in this experiment.
3. If calcium consumption is the same for women and men, there is a 3.5% chance that future studies will show differences in calcium consumption greater than observed in this study.
4. If calcium consumption is the same for women and men, there is a 3.5% chance that calcium consumption will be different in future experiments.

Question 2

Select one answer.

In 2011, the Institute of Medicine (IOM), a non-profit group affiliated with the US National Academy of Sciences, reviewed a study measuring bone quality and levels of vitamin-D in a random sample from bodies of 675 people who died in good health. 8.5% of the 82 bodies with low vitamin-D levels (below 50 nmol/L) had weak bones. Comparatively, 1% of the 593 bodies with regular vitamin-D levels had weak bones.

Medical researchers are conducting a double-blind experiment treating high blood pressure patients with a new vitamin supplement. The researchers are conducting a hypothesis test in which a Type I error is very serious, and the Type II error is not very serious. Which level of significance is the best choice?

1. α = 0.01
2. α = 0.05
3. α = 0.10

Answer 1

Answer:

Q1)

P-values indicate the believability that the null hypothesis is true given the sample data.

If the null hypothesis is correct, it is the probability of obtaining an effect at least as large as the one in your sample.

Therefore option C

If calcium consumption is the same for women and men, there is a 3.5% chance that future studies will show differences in calcium consumption greater than observed in this study.

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