Question

You took a poll of randomly selected 1,003 employees to ask how they feel about reversing the policy of working from home and switching to working in the office for the upcoming year. Of those polled, 37.2% of said “office.” How many respondents answered “office”? Give the point estimate. Construct a 95% confidence interval estimate (rounded to one decimal digit) of the percentage of all employees who would like to work at the office. Use a critical value of 1.96. Based on the hypothesis test, would you conclude that the majority (more than 50%) of the employees would like to come back to the office? Why or why not?

Answer 1

The number of respondents who answered 'office' is 372.216.

The 95% confidence interval estimate for the percentage of all employees who would like to work at the office is (34.2%, 40.2%).

Based on the hypothesis test, we conclude that the majority of employees do not want to come back to the office.

Step-by-step explanation:

a) To find the number of respondents who answered 'office,' we can multiply the percentage by the total number of respondents. Therefore, the number of respondents who answered 'office' is 0.372 * 1003 = 372.216.

For constructing a confidence interval, we can use the formula: Point Estimate ± (Critical Value * Standard Error). The point estimate is 37.2% and the critical value for a 95% confidence level is 1.96.

b) To calculate the standard error, we can use the formula: sqrt((p*(1-p))/n), where p is the point estimate and n is the sample size.

Therefore, the standard error is sqrt((0.372*(1-0.372))/1003) ≈ 0.0157.

Plugging these values into the confidence interval formula, we get: 0.372 ± (1.96 * 0.0157) = (0.342, 0.402).

This means that we can be 95% confident that the true percentage of all employees who would like to work at the office falls within the range of 34.2% to 40.2%.

c) To determine if the majority of employees would like to come back to the office, we can compare the confidence interval to a threshold of 50%.

Since the lower bound of the confidence interval, 34.2%, is less than 50%, we would conclude that the majority of employees do not want to come back to the office based on this hypothesis test.