Question

5. According to an official statement released by the state of California, the average height of a Redwood tree in California is 350 ft. To assess this claim, a scientist collects a sample of 50 randomly chosen Redwood trees in California. She finds that the average heights in her sample is 355 ft. We assume it is known that the population standard deviation is 42 ft (a) Conduct a hypothesis test to assess whether the true average height is 350 ft or if it higher. Use a0.1 (b) Find the p-value for the sample.

Answer 1

a)

null hypothesis:Ho Alternate Hypothesis:Ha 350 1.28 for 0.1 level with right tailed test, critical value of z= Decision rule: reject Ho if test statistic z>1.282 X= population mean sample mean sample size population std deviation 350 355.0000 50.00 42.000 standard errror of mean = Ox=0/Vn= 5.94 test statistic z = (x-1)/0,= 0.84

as test statistic is not greater than critical value, we fail to reject null hypothesis.

We can not conclude that true average height is greater than 350 ft.

b)

for above test statistic p value =0.2005