Question

According to a recent survey of 1,200 people, 61% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable job.

a. Define the random variables X and P′ in words.

b. Which distribution should you use for this problem? Explain your choice.

c. Construct a 90% confidence interval for the population proportion of people who feel the president is doing an acceptable job.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

Short answer

a. $X$and $P^{\mathrm{\prime }}$denote the individuals.

b. Distribution is out of$1200$individuals.

c. (i) $CI=(0.58684,0.63316)$

(ii) The graph has been shown

(iii) $EBM=0.02316$

Step-by-step solution

part (a) Explanation

The individuals who feel that the president is doing an acceptable job are denoted by $X$.

$P^{\mathrm{\prime }}$denotes the individuals who think the president is doing a suitable job.

part (b) explanation

Distribution is out of $1200$individuals

role="math" localid="1650865312144" $\Rightarrow N\left(0.61,\sqrt{\frac{0.61\times 0.39}{1200}}\right)$

part (c) explanation

(i) The confidence interval is

$x=732,n=1200$

Confidence level is$90\%$

$\Rightarrow (0.58684,0.63316)$

(ii) The graph is shown

(iii) The error bound is

$\begin{array}{r}EBM=\left(\frac{\text{Upper limit-lower limit}}{2}\right)\\ EBM=\left(\frac{0.63316-0.58684}{2}\right)\end{array}$

$\Rightarrow EBM=0.02316$