Testing Hypotheses About Proportions
32. Acid rain. A study of the effects of acid rain on trees in the Hopkins Forest shows that 25 of 100 trees sampled exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmentrics article on the average proportion of damaged trees in the Northeast. Does the sample suggest that trees in the Hopkins Forest are more susceptible than trees from the rest of the region? Comment, and write up your own conclusions based on an appropriate confidence intervals as well as a hypothesis test. Include any assumptions you made about the data.
Please show me the conditions and the steps...
THANKS!!!
I cant figure out this question...?
2008-08-18 8:44 pm
回答 (3)
2008-08-18 10:07 pm
✔ 最佳答案
ANSWER: To significance level of 99%, more than 0.15 (15%) damaged trees in Hopkins ForestPOPULATION PROPORTION HYPOTHESIS TESTING, NORMAL DISTRIBUTION, 7-Step Procedure
1. PARAMETER OF INTEREST: p = POPULATION PROPORTION
2. HYPOTHESES :
NULL HYPOTHESIS H0: p = 0.15 (15% DAMAGED TREES)
ALTERNATIVE HYPOTHESIS H1: p > 0.15 (exceeding 15% DAMAGED TREES)
3. COMPUTATION OF POPULATION PARAMETER:
STANDARD DEVIATION σ = sqrt[ p * ( 1 - p) / n ]
n = sample size [100]
σ = sqrt [0.15 * (1 - 0.15)/100] = 0.035707142
4. COMPUTATION OF TEST STATISTIC ("critical value of z")
z = (p_hat - p) / σ
p_hat = SAMPLE PROPORTION [0.25] (25/100)
z = (0.25-0.15)/ 0.035707142 = 2.8
Valid when both conditions true:
n * p > 10 [100 *0.15 = 5 > 10] TRUE
n (1 − p) > 10 [100 * (1 - 0.15) = 85 > 10] TRUE
5. "P-value" "Look-up" value of Normal Distribution "area under the curve" "to the right" of z = 2.8
"P-value" = 0.0026
6. TEST of P-value
P-value ≤ α (significance level) [0.0026 ≤ 0.01]; reject NULL HYPOTHESIS stating proportion of damaged trees = 0.15 (15%) for any reasonable significance level.
"When P-value is low, let it go" (let go the NULL HYPOTHESIS) P-value ≤ α
"When P-value is high, let it fly" (let fly the NULL HYPOTHESIS) P-value > α
7. CONCLUSION:
For signficance level α = 0.01, NULL HYPOTHESIS H0: p = 0.15 (15% damaged trees) should be rejected. More than 0.15 (15%) damaged trees.
2016-10-13 3:50 pm
he's a gorgeous horse, yet you're suitable, there is a few thing incorrect. in case you look on the attitude of his front pasterns and the hooves, you will see that the two legs are distinctive. He could be club-footed, or he would have been the sufferer of an extremely damaging farrier. The greater suitable hoof and pastern look like they are greater upright than the nearer one. mutually as this would merely be some thing it rather is unique to him by using a conformational deformity, i'd shop faraway from him for breeding or overall performance.
2008-08-18 8:50 pm
yes they are more susceptible because it is a 25% to 15% chance of being damaged.
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