Question

A medical website states that 40% of U.S. adults are registered organ donors. A researcher believes that the proportion is too high and wants to test to see if it is lower. She selects a random sample of 200 adults and finds that 74 of them are registered organ donors. Perform the hypothesis test at the 0.05 level. Compute the P-value and state a conclusion.

Answer 1

P value is 0.1932

conclusion is that find value P greater than hypothesis test at the 0.05 level

Explanation:

Given data

registered organ donors P = 40%

sample n = 200

registered organ donors x = 74

hypothesis test α = 0.05

to find out

P-value and state a conclusion

solution

we take a trail p less than 40 % i.e 0.40

so p = x/n

p = 74 / 200 = 0.37

so we find here Z value i.e

Z = p - P / √(PQ/n)

here Q = 1-p = 1-0.40 = 0.60

so Z = 0.37 - 0.40 / √(0.40×0.60/200)

Z = - 0.866

so p value for Z (-0.866) from z table

P value is 0.1932

and conclusion is that find value P greater than hypothesis test at the 0.05 level

Answer 2

Explanation:

Given:

n = 200

H0 : P = 40%

x = 74

a = 0.05

p' =
`(74)/(200) * 100 =` 37%

q' = 100 - p' = 100%- 37% = 63%

The Z score will be:

`Z = \frac{p'-P}{\sqrt{(p'.q')/(n)}} = \frac{37-40}{\sqrt{(37*63)/(200)}}`

Z = -0.8787

From the distribution table,

p- value = 0.1932

Since our pvalue(0.1932) is greater than significance level(0.05), we fail to reject the null hypothesis. We can now say statistically, there is not enough evidence to conclude that the proportion of registered donors is less than 40%