A survey of 2306 adult Americans aged 18 and older conducted by Harris

osnomu3

osnomu3

Answered question

2021-12-24

A survey of 2306 adult Americans aged 18 and older conducted by Harris Interactive found that 417 have donated blood in the past two years. (a) Obtain a point estimate for the population proportion of adult Americans aged 18 and older who have donated blood in the past two years. (b) Verify that the requirements for constructing a confidence interval about p are satisfied. (c) Construct a 90% confidence interval for the population proportion of adult Americans who have donated blood in the past two years. (d) Interpret the interval.

Answer & Explanation

Tiefdruckot

Tiefdruckot

Beginner2021-12-25Added 46 answers

Given:
n=2306
x=417
a) A point estimate of the population is the sample proportion.
The sample proportion is the number of successes divided by the sample size:
p^=xn=41723060.1808
b) Requirements to contruct confidence interval for p:np^(1p^)10 and sample is less than 5% of the population.
np^(1p^)=2306(0.1808)(10.1808)=341.5447961610
The condictions are verified, thus ut appropriate to construct a confidence interval for the population proportion p.
c) 90%=0.90
For confidence level 1α=0.90, determine zα2=z0.05 using the normal probability table in the appendix:
zα2=1.645
The margin of error is then:
E=zα2p^(1p^)n=1.645×0.1808(10.1808)2306
The boundaries of the confidence interval are then:
p^E=0.18080.0132=0.1676
p^+E=0.1808+0.0132=0.1940
d) We are 90% confident that the population proportion of adult Americans who have donated blood in the past two years is between 0.1676 and 0.1940

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