Question

The recommended dietary allowances of iron for women under the age of 51 is 18 milligrams (mg) per day. A medical researcher studying women living in a certain region suspected that the women were getting less than the daily allowance of iron, on average. The researcher took a random sample of women under the age of 51 from the region and measured their daily iron intakes. The following hypotheses were tested at the significance level of α = 0.05 for the population mean µ of the daily iron intake for women in the region.
H0: µ = 18
HA: µ < 18
All conditions for inference are met, and the resulting p-value was 0.031.
Which of the following is an appropriate conclusion?

(A)   The p-value is less than α, and the null hypothesis should be rejected. There is convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg.

(B)   The p-value is less than α, and the null hypothesis should be rejected. There is not convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg.

(C)   The p-value is less than α, and the null hypothesis should not be rejected. There is not convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg.

D-The p-value is greater than α, and the null hypothesis should be rejected. There is convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg.

E-The p-value is greater than α, and the null hypothesis should not be rejected. There is not convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg.

Answer 1

Conclusion on p-value:

Given,

hypotheses were tested at the significance level of α = 0.05 And p-value = 0.031

So, P-value (0.031) is less than 0.05 then reject H0.

The alternative hypothesis is HA: µ < 18

i.e.population mean µ of the daily iron intake for women in the region is less than the recommended 18 mg.

So, Answer A is correct.

(A)   The p-value is less than α, and the null hypothesis should be rejected. There is convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg.