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

mu = 26 gm

Std error = rt 81/rt 100 = 0.9

Confidence Interval:

Margin of error = 1.96(std error)

=±1.76

Range for the true population mean:

21.74 to 25.26

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Hypothesis testing:

H0: x bar = 26

Ha: xbar <26

Left tailed test

For 99%

Confidence Interval:

±2.32

Range for the true population mean:

21.18 to 25.82

As 26 does not fall in 99% confidence interval, we reject null hypothesis.,as there is evidence that the current mean weight is less than 26 gm