Question

a survey of 2284 adults in a certain large country aged 18 and older conducted by reputable polling organization founded that 424 have donated blood in the past two years. Complete Parts (a) through (C).
a) obtain a point estimate for the population proportion of adults in the country age 18 and older who have donated blood in the past two years.

b) verify that the requirements for constructing a confidence interval.
the sample [ a) can be assumed to be b)is stated to not be. c) cannot be assumed to be. d) is stated to be. ] a simple random sample, the value of [ a)np b) p(1-p) c) np(1-p) d) p.] is [ ]. which is [ a) greater than. b) less then] 10. & the [ a) population size b) sample population c) sample size d) population proportion] [ a)can be assumed to be. b) is stated to not be c) cannot be assumed to be d) is stated to] less than or equal to 5% of the [a) sample proportion b) population proportion c) population size d) sample size.]

c. construct and interpret a 90% confidence interval for the population proportion of adults in the country who have donated blood in the past two years. Select the correct Choice below and fill in any answer box within your choice.( type integer or decimal rounded to three decimal places as needed. Use ascending order)
A) we are [ ]% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between [ ] and [ ].
B) there is a [ ]% chance the proportion of adults in the country aged 18 and older who have donated blood in the past 2 years is between [ ] and [ ].

Answer 1

(a) The point estimate for the population proportion of adults in the country age 18 and α/αolder who have donated blood in the past two years = p^ =X/N = No. of people who donated blood/ Total No of people surveyed

So, p^=424/2284=0.1856

(b) The sample (a) can be assumed to be a simple random simple random sample, the value of (a) np is (a)greater than 10 & the (c)sample size [ a)can be assumed to be less than or equal to 5% of the (c) population size

© For 90% CI, 1-α=0.90=> α=1-0.90=0.10.

CI for proportion is given by

p^± Z(α/2)*√{p^(1-p^)/n}

Now p^=0.1856 (From part (a))

√{p^(1-p^)/n}=√{0.1856*(1-0.1856)/2284}=0.0081

Z(α/2)=Z(0.10/2)=Z(0.05)=1.65 (From normal table)

Hence the 90% CI is

0.1856±1.65*0.0081

i.e, 0.1856±0.1337

i.e (0.052,0.319) (Ans)

Hence, [A] we are 90% confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between [0.052] and [0.319].