a) A clinical trial was conducted and in a randomized sample of 305 patients the medicine was found to give satisfactory relief from allergy for 241 patients. Determine a 95% confidence interval for the proportion of the patient population that is likely to find relief with the treatment. The manufacturer’s advertising statement claims that 88% of patients are treated successfully. Use your confidence interval to examine this claim.
b) in a paired feeding experiment, the gains in weight in kg of small animals fed on two different diets are:
Pair 1 2 3 4 5
Diet X 4.4 3.8 3.3 4.0 3.5
Diet Y 4.4 3.1 2.9 4.2 2.9
Test if there is any real difference in average weight gains due to the two diets.
statistic mathematics uni
2009-08-05 10:44 pm
回答 (3)
2009-08-06 3:06 am
✔ 最佳答案
a) p'=241/305=0.7902. a 95% confidence interval isp'-1.96√[p'(1-p')/n]<p<p'+1.96√[p'(1-p')/n]
0.7902-1.96√[0.7902(0.2098)/305]<p<0.7902+1.96√[0.7902(0.2098)/305]
0.7445<p<0.8359
Since the upper limit of p is 83.59%, so we reject the manufacturer’s advertising statement.
b)
Pair 1 2 3 4 5
Diet X 4.4 3.8 3.3 4.0 3.5
Diet Y 4.4 3.1 2.9 4.2 2.9
Difference 0 0.7 0.4 -0.2 0.6
Mean=(0+0.7+0.4-0.2+0.6)/5=0.3
Variance=0.12,s=0.3464
H0: No difference between two diet.
H1: Reject H0
alpha=0.05, t(4,0.025)=2.78
Test-statistic=|0.3-0|/(0.3464/√5)=1.9365
Since 1.9365<2.78, do not reject H0 and conclude that there is no real difference in average weight gains due to the two diets.
2009-08-06 1:16 am
it didnt provided.but in my opinion in part a it said that 95% confidence interval so it may be 5 % significance level.
2009-08-05 11:39 pm
For (b), any significance level (say 1% or 5%) provided?
收錄日期: 2021-04-26 13:44:36
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