Question

1. careful genetic engineering, you have produced what you call the Super Tree – a tree that can absorb extraordinary amounts of carbon dioxide (CO₂), thereby helping to slow the process of global warming. Past research has shown that a regular tree absorbs 48 pounds of (CO₂) per year but you find that in a random sample of 16 of your own Super Trees, the average amount of CO₂absorbed is 54.3 pounds with a standard deviation of 18. Using an alpha (α) level of .10, test the hypothesis that the average CO₂absorption in your population of Super Trees is better than the typical tree.

1. (1 point) In symbols, what is the null hypothesis for this test? ___________________

2. (1 point) In words, what is the null hypothesis for this test? _____________________

3. (1 point) In symbols, what is the alternative hypothesis for this test? _____________

4. (1 point) In words, what is the alternative hypothesis for this test? _______________

5. (1 point) Is this a one-sided or two-sided test? How do you know? ________________

6. (1 point) Will you use a z-test or a t-test in this situation? Why? __________________

7. (1 point) What is the critical value of the test statistic? __________________________

8. (4 points) What is the value of the test statistic calculated from the sample results?

9. (2 points) What is your decision about the null hypothesis, and what does this indicate about the CO₂ absorption of your Super Trees? _______________________________

Answer 1

a)

b) H₀: The regular tree absorbs of (CO2) per year is 48 pounds.

c)

d) H₁: The regular tree absorbs of (CO2) per year is greater than 48 pounds.

e) This is a one-sided test.

f) We will use t-test, because is unknown and the sample size is less than 30.

g) The critical value is t_0.1,15 = 1.341

h) The test statistic is

i) Since the test statistic value is greater than the critical value, so we should reject the null hypothesis.

At 0.10 significance level, there is sufficient evidence to conclude that the average Co2 absorption in the population of Super Trees is better than the typical tree.