Does the growth of trees vary more when the trees are young? The international t

Question

Does the growth of trees vary more when the trees are young? The international tree ring data base collected data on a particular 440 year old douglas fir tree. The standard deviation of the annual tree growth in the trees first 80 years of life was .8 millimeters per year. Assume that the population is normal. We are interested in testing whether the population standard deviation of annual ring growth in the trees later years is less than 0.0 mm/year. The sample variance of the ring growth for a random sample of size 100 taken from the trees later years =.3136 square mm. Use hypothesis testing to solve.

Explanation / Answer

Given that

Sample size n=100

Population standard deviation sigma=0.8

Sample variance S^2 = 0.3136

H0:sigma =0.8

H1 : sigma <0.8

Significance level alpha=0.05

From chi-square table the critical value =77.0463

Therefore, the critical region is Chi-square < 77.0463

The test statistic is

                Chi-square = (n-1)S^2/sigma^2 which follows a chisquare distribution with 99 d.f

Substituting we get

Chi-square = 99*0.3136/(0.8*0.8) =48.51

P value = 0.0000

Since the value of the test statistic is in the critical region we reject the null hypothesis at 5% level of significance.

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