Question

Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. A random sample of 2000 women from the first country yielded 439 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 316 women with iron-deficiency anemia. Can we conclude, at the 0.05 level of significance, that the proportion of women with anemia in the first country is greater than the proportion of women with anemia in the second country?Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Null Hypothesis: ?

Alternative Hypothesis: ?

Type of test statistic: ? (z, t, chi square, F)

The value of the test statistic: ? (round to 3 decimal places)

The p-value: ? (round to 3 decimal places)

Can we conclude that the proportion of women with anemia in the first country is greater than the proportion of women with anemia in the second country? (yes or no)

Answer 1

p₁: Population proportion of women with iron-deficiency anemia in Country 1

p₂ : Population proportion of women with iron-deficiency anemia in Country 2

Null hypothesis : proportion of women with anemia in the first country is equal to the proportion of women with anemia in the second country i.e p₁=p₂ ; p₁-p₂ =0

Alternate Hypothesis : Proportion of women with anemia in the first country is greater than the proportion of women with anemia in the second country ; p₁ > p₂ ; p₁-p₂ > 0

H_o : p₁ - p₂ = 0

H_a : p₁ - p₂ > 0 (Right Tailed test)

Type of Statistic : Z

	Country 1	Country 2
Number of women in the sample(n)	n1=2000	n2=1700
Number of women with iron-deficiency anemia(x)	x1=439	x2=316
Sample proportion of Proportion of women with iron-deficiency anemia	=439/200=0.2195	==316/1700=0.1859

The value of the test statistic = 2.5271

For Right tailed test:

p-value = 0.0058

As P-Value i.e. is less than Level of significance i.e (P-value:0.0058 < 0.05:Level of significance); Reject Null Hypothesis

At 0.05 level of significance , There is sufficient evidence to conclude that  that the proportion of women with anemia in the first country is greater than the proportion of women with anemia in the second country

Can we conclude that the proportion of women with anemia in the first country is greater than the proportion of women with anemia in the second country? (yes or no)

Ans : Yes