Question

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?

Answer 1

Answer:

0.035 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis & accept the alternative hypothesis conclude that there is a significant difference between the proportion of the U.S. women residents consuming recommended levels of calcium and proportion of the U.S. men residents consuming recommended levels of calcium.

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and is always about the absence of significant difference between two proportions being compared.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared.

For this question, we are comparing the proportion of U.S. residents consuming recommended levels of calcium among women and men.

We want to check if there is a significant difference between the proportion of the U.S. women residents consuming recommended levels of calcium and proportion of the U.S. men residents consuming recommended levels of calcium.

If the proportion of U.S. women residents consuming recommended levels of calcium = p₁

And

the proportion of U.S. men residents consuming recommended levels of calcium = p₂

And the difference between them is given as

μ₀ = p₁ - p₂

The null hypothesis and alternative hypothesis can be expressed mathematically as

The null hypothesis that there is no significant difference between the proportion of the U.S. women residents consuming recommended levels of calcium and proportion of the U.S. men residents consuming recommended levels of calcium

H₀: μ₀ = 0

or

H₀: p₁ = p₂

And the alternative hypothesis that there is a significant difference between the proportion of the U.S. women residents consuming recommended levels of calcium that are women and proportion of the U.S. men residents consuming recommended levels of calcium that are men

Hₐ: μ₀ ≠ 0

or

Hₐ: p₁ ≠ p₂

So, to interpret the p-value now,

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?

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 5% = 0.05

p-value = 0.035

0.035 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis & accept the alternative hypothesis conclude that there is a significant difference between the proportion of the U.S. women residents consuming recommended levels of calcium and proportion of the U.S. men residents consuming recommended levels of calcium.

Hope this Helps!!!