Answer: a. 0.542
b. 0.051
c. [tex](0.491,\ 0.593)[/tex]
Step-by-step explanation:
Let p be the population proportion of parents spend too little time with their children because of work commitments
As per given , we have
n= 369
[tex]\hat{p}=\dfrac{200}{369}=0.542005420054\approx0.542[/tex]
Since the sample proportion is the best estimate for the population proportion.
So , the point estimate of the proportion of the population of working parents who feel they spend too little time with their children because of work commitments = 0.542
z-value for 95% confidence interval : [tex]z_{\alpha/2}=1.96[/tex]
Margin of error : [tex]E=z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]E=(1.96)\sqrt{\dfrac{0.542(1-0.542)}{369}}\\\\=0.0508364564574\approx0.051[/tex]
The margin of error = 0.051
Confidence interval : [tex]\hat{p}\pm E[/tex]
[tex]0.542\pm0.051\\\\=(0.542-0.051,\ 0.542+0.051)\\\\=(0.491,\ 0.593)[/tex]
95% confidence interval estimate of the population proportion of working parents who feel they spend too little time with their children because of work commitments : [tex](0.491,\ 0.593)[/tex]
