Question

NEED HELP ASAP - will give thumbs up

Multi part question set

If you can’t finish all of it, that’s ok!

Would really appreciate any and all help as soon as possible

Thank you so much in advance!

Thank you!! Telecommuting - 1, NUMERICAL ANSWER There are 5 questions in this set. As you proceed through these questions, use necessary information in the previous questions. In the year 2023, a labor economist is interested in the change in the fraction of workers who telecommuted (worked from home) from 2020 to 2023. In a random sample of 400 office workers from 2020, 140 of these workers telecommuted. In an independent random sample of 500 office workers from 2023, 120 of these workers telecommuted. To begin, the economist decides to calculate a confidence interval for the difference between the fraction of office workers who telecommuted in 2023 (the "X" population) and the fraction of office workers who telecommuted in 2020 (the "Y" population). Calculate the lower (smaller) endpoint of the 95% confidence interval for the difference between the fraction of office workers who telecommuted in 2023 and the fraction of office workers who telecommuted in 2020. Three decimals Continued. Calculate the upper (larger) endpoint of the 95% confidence interval. Three decimals 2

Answer 1

1. Lower endpoint=0.050

2. Upper endpoint=0.167

3. The answer is the last option. THREE

4. Reject

5. Minimum necessary value=8537

------------------------------------------------------------------------------------------------------------------------------------------------------------

The estimated proportions $\hat{p}_{x}=\frac{140}{400}=0.35,\hat{p}_{y}=\frac{120}{500}=0.24$

The confidence interval is given by

$CI=\hat{p}_{x}-\hat{p}_{y}\mp Z_{1-\alpha /2}\sqrt{\frac{\hat{p}_{x}(1-\hat{p}_{x})}{n_{x}}+\frac{\hat{p}_{y}(1-\hat{p}_{y})}{n_{y}}}$

$CI=0.35-0.24\mp 1.96\sqrt{\frac{0.35(1-0.35)}{400}+\frac{0.24(1-0.24)}{500}}$

$CI=0.11\mp 1.96\sqrt{\frac{0.35(0.65)}{400}+\frac{0.24(0.76)}{500}}$

$CI=0.11\mp 1.96\sqrt{0.000568+0.0003648}$

$CI=0.11\mp 1.96\sqrt{0.00093}$

$CI=0.11\mp 1.96*0306$

$CI=0.11\mp 0.0599$

$CI=(0.0501,0.16699)$