Question

A survey of 2303 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 407 have donated bloood in the past two years. Complete parts (a) through (c) below.

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A survey of 2303 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 407 have donated blo lick here to view page 1). Click here to view the standard normal distribution table (page 2). (a) Obtain a point estimate for the population proportion of adults in the country aged 18 and older who have donated blood in the past two years (Round to three decimal places as needed.) (b) Verify that the requirements for constructing a confidence interval about p are satisfied The sample ?-«Dwhich 10, and the V a simple random sample, the value of (Round to three decimal places as needed.) c onstruct and interpret a 90% confidence interval for the population proportion of adults in the country who have donated blood an the past two years Type integers or decimals rounded to three decimal places as needed Use ascending order ) an er who have donated blood an the past two years ?s between O A OB We are % confident the proportion of adults in the country aged 18 and o an Theresa % chance the proportion of adults in the country aged 18 and older who have donated bloodin the past two years s beteen Click to select your answer(s). Type here to search

Answer 1

a) $\widehat p$ = 407/2303 = 0.177

b) THe sample is stated to be a simple random sample, the value of n$\widehat p$(1 - $\widehat p$ ) is 335.48 which ig greater than 10 and the sample size is less than or equal to 5% of population size.

c) At 90% confidence interval the critical value is z_0.05 = 1.645

The 90% confidence interval is

$\widehat p$ +/- z_0.05 * sqrt($\widehat p$(1 - $\widehat p$ )/n)

= 0.177 +/- 1.645 * sqrt(0.177 * (1 - 0.177)/2303)

= 0.177 +/- 0.013

= 0.164, 0.190

Option - A) We are 90% confidedent that the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between 0.164 and 0.190

OPtion - B) There is 90% chance that the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between 0.164 and 0.190