Question

A random sample of small-business managers was given a leadership style questionnaire. The results were scaled so that each manager received a score for initiative. Suppose the following data are a random sample of these scores. 41 42 39 39 38 31 39 41 35 45 30 33 35 44 36 41 39 33 39 39 41 33 35 36 41 33 41 38 39 42 44 35 36 33 38 32 30 41 42 Assuming σ is 3.891, use these data to construct a 90% confidence interval to estimate the average score on initiative for all small-business managers.

___≤ μ ≤___

Answer 1

Solution-:

Given:

First we find sample mean by using R-Software :

>x=c(41,42,39,39,38,31,39,41,35,45,30,33,35,44,36,41,39,33,39,39,41,33,35,36,41,33,41,38,39,42,44,35,36,33,38,32,30,41,42);x
[1] 41 42 39 39 38 31 39 41 35 45 30 33 35 44 36 41 39 33 39 39 41 33 35 36 41
[26] 33 41 38 39 42 44 35 36 33 38 32 30 41 42
> n=length(x);n
[1] 39
> m=mean(x);m
[1] 37.66667

> round(m,2)
[1] 37.67

To construct a 90% confidence interval to estimate the average score on initiative for all small-business managers is as follows;

Where, (From Normal Probability Integral Table)

The required C.I. is,