In a recent survey142 of 453 employees responded that they t

In a recent survey,142 of 453 employees responded that they typically took work with them on vacation and

89 responded that there are unwritten and unspoken expectations that they stay connected. Complete parts (a) through (c) below.

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

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.

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 say there are unwritten and unspoken expectations that they stay connected on vacation lies within the interval in (b).

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 (b).

C. 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).

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 (b).

Solution

a)
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=142
Sample Size(n)=453
Sample proportion = x/n =0.3135
Confidence Interval = [ 0.3135 ±Z a/2 ( Sqrt ( 0.3135*0.6865) /453)]
= [ 0.3135 - 1.64* Sqrt(0.0005) , 0.3135 + 1.64* Sqrt(0.0005) ]
= [ 0.2778,0.3492]

b)
Mean(x)=89
Sample Size(n)=453
Sample proportion = x/n =0.1965
Confidence Interval = [ 0.1965 ±Z a/2 ( Sqrt ( 0.1965*0.8035) /453)]
= [ 0.1965 - 1.64* Sqrt(0.0003) , 0.1965 + 1.64* Sqrt(0.0003) ]
= [ 0.1659,0.2271]

c)
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).

d)
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 (b).