Question

In a survey of​ employees, a company reported that 52​% had confidence in the actions of senior management. To be 95​% confident that at least half of all employees have confidence in senior​ management, how many would have to be in the survey​ sample?

Please show and explain work

Answer 1

Answer:-

Given that:-

In a survey of​ employees, a company reported that 52​% had confidence in the actions of senior management. to be 95​% confident that at least half of all employees have confidence in senior​ management,

In a survey of employees, 52% had confidence in  actions of senior management at 95% confidence level

That is, the sample proportion,

The confidence  level,

Find the number of employees in the survey.

It is given that, level of the significance ,

The remaining 5%s divided into two  equal half's, that is, 0.025% for left region and 0.025% for right region Since it is two .tailed test need to consider only one half of the critical region, that is, need to consider only 0.025. Therefore, the total probability would be

Determine the critical value using excel function.

Margin of error is 0.01 which is taken from  the sample sizes needed for several choice of margin of error table due to large  sample size.

Determine the sample size using the formula

Here, is the sample proportion ,M.E is the margin of error and is the critical value

Substitute the values and in the above equation .

Therefore ,the number of employees in our survey is