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.374243393831433735453033354436373933394341333536413337384342443536333832303742 Assuming σ is 4.210, use these data to construct a 90% confidence interval to estimate the average score on initiative for all small-business managers.Appendix A Statistical Tables(Round the intermediate values to 3 decimal places, e.g. 25.316. Round your answers to 3 decimal places, e.g. 25.316.)enter the lower value of the interval ≤ μ ≤ enter the upper value of the interval

We have to find confidence interval for population mean (μ) Since population standard deviation (σ) know we have to use standard normal distribution. formula : CI = x¯ ± zα/2×σn Where , zα/2 is critical value for given confidence level. σ is population standard deviation x¯ is sample mean n is sample size Given data , 37 42 43 39 38 31 43 37 35 45 30 33 35 44 36 37 39 33 39 43 41 33 35 36 41 33 37 38 43 42 44 35 36 33 38 32 30 37 42 Sample size = n = 39 Population standard deviation = σ = 4.210 Let's find sample mean ( x¯ ) x¯ = ∑xin x¯ = 37+42+43+39+38+31+43+..........+ 32+30+37+4239 x¯ = 37.5641026 Now let's find critical value (zα/2) Confidence level = 90% = 0.9 Significance level = α = 1 - 0.9 = 0.1 , α/2 = 0.1/2 = 0.05 So, critical value = zα/2= 1.6449 ---> Using Excel , =NORMSINV(1-0.05) = 1.6449 Put values in formula, we get CI = x¯ ± zα/2×σn CI = 37.5641026± 1.6449×4.21039 CI = 37.5641026± 1.108892109 CI = (36.4552105, 38.6729947) A 90% confidence interval to estimate the average score on initiative for all small-business managers is , 36.455≤μ≤ 38.673

Answered: A random sample of small-business…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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.

37	42	43	39	38	31	43
37	35	45	30	33	35	44
36	37	39	33	39	43	41
33	35	36	41	33	37	38
43	42	44	35	36	33	38
32	30	37	42

Assuming σ is 4.210, use these data to construct a 90% confidence interval to estimate the average score on initiative for all small-business managers.

Appendix A Statistical Tables

(Round the intermediate values to 3 decimal places, e.g. 25.316. Round your answers to 3 decimal places, e.g. 25.316.)

enter the lower value of the interval ≤ μ ≤ enter the upper value of the interval

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