Question

estimate part time monthly salary based on a sample of 5 students as shown 1200, 2000, 800, 500, 700 what is the mean? calculate s and construct 90% confidence interval for the average income

please use example Xi Xi-Xbar (Xi-Xbar)squared to show answers

Answer 1

Answer)

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

Mean = 1040

S.d = 594.138

As the population s.d is unknown and we are using the sample s.d as the best estimate

We can use t distribution to construct the interval

Degrees of freedom is = n-1 = 5-1 = 4

For 4 df and 90% confidence level

Critical value t from t table is = 2.13

Margin of error (MOE) = t*s.d/√n = 2.13*594.138/√5 = 566.45

Confidence interval is given by

[Mean - MOE, Mean + MOE]

[473.55, 1606.45].

We are 90% confident that the population mean (μ) falls between 473.55 and 1606.45.