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Confidence intervals for employees who took work on vacation

In a recent survey, 161 of 493 employees responded that they typically took work with them on vacation and 95 responded that there are unwritten and unspoken expectations that they stay connected.

a. Construct a 90% confidence interval estimate for the population proportion of employees who typically take work with them on vacation.
__ <= pi <= __

b. Construct a 90% confidence interval estimate for the population proportion of employees who said that there are unwritten and unspoken expectations that they stay connected.
__ <= pi <= __

c. Interpret the intervals in (a) and (b). Which of the following is the correct interpretation for the interval in (a)?
A You can be 90% confident that the population proportion of the employees surveyed that take work with them on vacation lies within the interval in (a).
B. You can be 90% confident that the population proportion of all employees that take work with them on vacation lies within the interval in (a).
C. You can be 90% confident that the population proportion of the employees surveyed that say there are unwritten and unspoken expectations that they stay connected on vacation lies within the interval in (a).
D. You can be 90% confident that the population proportion of all employees that say there are unwritten and unspoken expectations that they stay connected on vacation lies within the interval in (a).

Which of the following is the correct interpretation for the interval in (b)?
A. You can be 90% confident that the population proportion of the employees surveyed that take work with them on vacation lies within the interval in (b).
B. You can be 90% confident that the population proportion of all employees that say there are unwritten and unspoken expectations that they stay connected on vacation lies within the interval in (b).
C. You can be 90% confident that the population proportion of the employees surveyed that say there are unwritten and unspoken expectations that they stay connected on vacation lies within the interval in (b).
D. You can be 90% confident that the population proportion of all employees that take work with them on vacation lies within the interval in (b).

d. Explain the difference in the results in (a) and (b). Choose the correct answer below.
A. The two confidence interval estimates overlap because the two separate point estimates are far enough apart.
B. The two confidence interval estimates do not overlap because the two separate point estimates are far enough apart.
C. The two confidence interval estimates overlap because the two separate point estimates are close enough together.
D. The two confidence interval estimates do not overlap because the two separate point estimates are close enough together.

Solution Preview

Please find the attached answer.

a. (0.29, 0.36)
b. (0.16, 0.22)
c. first part: Answer A
Comment: Confidence intervals refer to the population from which the sample comes. Thus, ...

Solution Summary

The confidence intervals for employees who took work on vacation are examined.

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