Question

The CEO of a large corporation asks his Human Resource (HR) director to study absenteeism among its executive-level managers at its head office during the year. A random sample of 30 executive level managers reveals the following: Absenteeism: Sample mean = 7.3 days, Sample standard deviation=6.2 days 18 mid-level managers out of the 30 randomly selected mid-level managers, cite stress as a cause of absence. (a) Construct a 90% confidence intervalestimate for the mean number of absences for mid- level managers during the year.(b) Construct a 98% confidence intervalestimate for the population proportion of mid-level managers who cite stress as a cause of absence. (c) What sample size is needed to have 95% confidence in estimating the population mean absenteeism to within 1.5 days if the population standard deviation is estimated to be 8 days? (d) How many mid-level managers need to be selected to have 99% confidence in estimating population proportion of mid-level managers who cite stress as a cause of absence to within +0.075 if no previous estimate is available?

Answer 1

Answer:

Following are the answer to this question:

Step-by-step explanation:

Given:

n = 30 is the sample size.  

The mean  $\bar X$ = 7.3 days.  

The standard deviation = 6.2 days.  

df = n-1  

     $= 30-1 \\ =29$

The importance level is $\alpha$ = 0.10  

The table value is calculated with a function excel 2010:

$= tinv (\ probility, \ freedom \ level) \\= tinv (0.10,29) \\ =1.699127\\ = t_{al(2x-1)}= 1.699127$

The method for calculating the trust interval of 90 percent for the true population means is:

Formula:

$\bar X - t_{al 2,x-1} \frac{S}{\sqrt{n}} \leq \mu \leq \bar X+ t_{al 2,x-1} \frac{S}{\sqrt{n}}$

$=\bar X - t_{0.5, 29} \frac{6.2}{\sqrt{30}} \leq \mu \leq \bar X+ t_{0.5, 29} \frac{6.2}{\sqrt{30}}\\\\=7.3 -1.699127 \frac{6.2}{\sqrt{30}}\leq \mu \leq7.3 +1.699127 \frac{6.2}{\sqrt{30}}\\\\=7.3 -1.699127 (1.13196)\leq \mu \leq7.3 +1.699127 (1.13196) \\\\=5.37 \leq \mu \leq 9.22$

It can rest assured that the true people needs that middle managers are unavailable from 5,37 to 9,23 during the years.