Question

The herbal supplement biloba ginko is advertised as producing an increase in physical strength and stamina. To test this claim, a sample of n = 27 adults is obtained and each person is instructed to take the regular dose of the herb for 45 days. At the end of the 45-day period, each person is tested on a standard treadmill task for which the average score for the population is µ = 18. The individuals in the sample produce a mean score of M = 21.2 with SS = 1460.

1.) Are these data sufficient to conclude that the herb has a statistically significant effect on stamina using a two-tailed test with alpha = .05? Be specific here (in other words, reject or retain the null and why and then interpret what that means). Make sure to show all four (or five) steps.

2.) What decision would be made if the researcher used a one-tail test with alpha = .05 and why? Be specific.

Answer 1

x = 21.2, s2 = 1460, n= 27, µ = 18

1. H0: µ = 18, Herb does not have a statistically significant effect on stamina

H1: µ ≠ 18, Herb has a statistically significant effect on stamina

Test statistic: t = (x-µ)/(s2/n)^0.5

= (21.2-18)/(1460/27)^0.5

= 0.435

α = 0.05

Degrees of freedom: df = n-1 = 27-1 = 26

Critical t = tα,df = t0.05,26 = 2.056

Since test statistic is less than critical value, we reject the null hypothesis and conclude that herb does not have a statistically significant effect on stamina.

2. H0: µ = 18, Herb does not have a statistically significant effect on stamina

H1: µ > 18 or µ < 18, Herb has a statistically significant effect on stamina

Test statistic: t = (x-µ)/(s2/n)^0.5

= (21.2-18)/(1460/27)^0.5

= 0.435

α = 0.05

Degrees of freedom: df = n-1 = 27-1 = 26

Critical t = tα/2,df = t0.025,26 = 1.706

Since test statistic is less than critical value, we reject the null hypothesis and conclude that herb does not have a statistically significant effect on stamina.