Question

A data set of samples is given below. Use a 0.05 significance level to test the claim that the samples are from a population with a mean that is less than 0.065.

1. Write Ho (null) and H1 (alternative) and indicate which is being tested

2. Describe the statistical test chosen

Data Set

0.066

0.059

0.058

0.058

0.076

0.082

0.053

0.053

0.072

0.076

0.066

0.084

0.05

0.051

0.068

0.065

0.084

0.078

0.082

0.056

0.066

0.081

0.08

0.053

0.068

0.06

0.077

0.062

0.055

0.05

0.052

0.07

0.051

0.059

0.052

0.058

0.065

0.058

0.074

0.071

0.083

0.062

0.063

0.084

0.077

0.056

0.073

0.085

0.082

0.065

0.071

0.076

Answer 1

(1) Ho: μ ≥ 0.065 and Ha: μ < 0.065

(2) Left-tailed t- test for a population mean

Data:    

n = 52   

μ = 0.065   

s = 0.011   

x-bar = 0.0668   

Hypotheses:    

Ho: μ ≥ 0.065   

Ha: μ < 0.065   

Decision Rule:    

α = 0.05   

Degrees of freedom = 52 - 1 = 51

Critical t- score = -1.675284951   

Reject Ho if t < -1.675284951   

Test Statistic:    

SE = s/√n = 0.011/√52 = 0.001525426

t = (x-bar - μ)/SE = (0.0668 - 0.065)/0.00152542553961938 = 1.179998599

Decision (in terms of the hypotheses):

Since 1.179998599 > -1.675284951 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that the mean < 0.065