Question

Suppose the following data are selected randomly from a population of normally distributed values. 46 51 43 48 44 57 54 39 40 48 45 39 45 Construct a 95% confidence interval to estimate the population mean. Appendix A Statistical Tables (Round the intermediate values to 2 decimal places. Round your answers to 2 decimal places.)

≤ μ ≤

Answer 1

Answer)

First we need to find the mean and s.d of the given data

Mean = 46.08

S.d = 5.53

N = 13

As the population standard deviation is unknown here we will use t distribution to construct the interval

Degrees of freedom is = n-1 = 12

For 12 dof and 95% confidence level, critical value t from t table is = 2.18

Margin of error (MOE) = t*s.d/√n = 2.18*5.53/√13 = 3.3417

Interval is given by

(Mean - MOE, Mean + MOE)

[42.7383, 49.4217].

You can be 95% confident that the population mean (μ) falls between 42.7383 and 49.4217.

42.74 < u < 49.42