Respuesta :
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!!!
From the hypothesis test, it can be concluded that since the p-value is of 0.035 < 0.05, there is enough evidence to conclude that the proportion of U.S. residents consuming recommended levels of calcium is different among women and men.
At the null hypothesis, it is tested if the proportion among men and woman is the same, that is:
[tex]H_0: \mu_M - \mu_W = 0[/tex]
At the alternative hypothesis, it is tested if the proportions are different, that is:
[tex]H_1: \mu_M - \mu_W \neq 0[/tex]
Since the p-value is of 0.035 < 0.05, there is enough evidence to conclude that the proportion of U.S. residents consuming recommended levels of calcium is different among women and men.
A similar problem is given at https://brainly.com/question/25147864
