A botantist is studying the drought response of the Texas Bu

A botantist is studying the drought response of the Texas Buckeye (Aesculus arguta) by weighing mature seed capsules. In a sample of n = 100 capsule weights, he observes the sample statistics x¯ = 23.5 gm s 2 = 81 gm2

(a) Find a 95% confidence interval for the average weight of a buckeye seed capsule.

(b) Our botanist suspects the mean weight he has observed is lower than normal. Published references suggest a mean weight of 26 gm. Test the research hypothesis that the current mean weight is less than 26 gm, using the sample data above. Use a Type I error of = 0.01 for your test.

Solution

a) 95% confidence interval for the average weight of a buckeye seed capsule.we consider t test for this and get confidence intervas as (21.714, 25.286)

b)

One-Sample Z

Test of mu = 26 vs not = 26
The assumed standard deviation = 9

N Mean SE Mean 99% CI Z P
100 23.500 0.900 (21.182, 25.818) -2.78 0.005