Question

A researcher has collected n = 1000 random water samples from a freshwater lake and the calcium concentration (milligrams per liter) were measured. A 95% confidence interval for the population mean calcium concentration was found to be [0.49, 0.82]. State a decision for the hypothesis test below (i.e. reject H0 or fail to reject H0) using this 95% confidence interval when testing the hypothesis at the α = 0.05 level. H0 : µ = 0.60 vs. H1 : µ 6= 0.60.

Answer 1

Decision rule is reject H0 is 0.60 does not lie in the confidence interval.

Explanation:

Given that a researcher has collected n = 1000 random water samples from a freshwater lake and the calcium concentration (milligrams per liter) were measured.

`H0 : \mu = 0.60 vs. \\H1 : \mu\\eq  0.60.`

(Two tailed test at 5%significant level)

95% confidence interval is given as

(0.49, 0.82)

We check whether our hypothesised mean belongs to this interval

0.60 lies inside the confidence interval

Hence we accept null hypothesis

Decision rule is reject H0 is 0.60 does not lie in the confidence interval.