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.

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

Appendix A Statistical Tables

(Round the intermediate values to 3 decimal places. Round your answers to 3 decimal places.)

______ ≤ μ ≤ _______

Answer 1

Since population standard deviation is known, Use z-distribution.

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

Refer Standard normal table/Z-table or use excel function "=NORM.S.INV((1-0.05))" to find the Z-value.