A researcher wishes to determine if the addition of nutritional yeast to the die
ID: 2923279 • Letter: A
Question
A researcher wishes to determine if the addition of nutritional yeast to the diet of dogs will reduce the degree of flea infestation. A sample of 50 dogs all suffering from chronic flea infestation were given the yeast additive for 1 week after which an assessment of the degree of infestation was made for each dog and reported as either an increase or decrease. In this study 36 of the dogs had a decrease in infestation.
A. Estimate the probability a dog will have a decrease in infestation and give its 95% confidence limits. Show your work.
B. Assume that if there is no effect of the yeast supplement one expects half the dogs to increase and half to decrease. Use a statistical test to determine if the yeast additive is effective in reducing flea infestation. Show your work and give the p-value.
If you use the software R, it would be helpful if you included your code so that I can compare to find where I went wrong.
Explanation / Answer
A researcher wishes to determine if the addition of nutritional yeast to the diet of dogs will reduce the degree of flea infestation. A sample of 50 dogs all suffering from chronic flea infestation were given the yeast additive for 1 week after which an assessment of the degree of infestation was made for each dog and reported as either an increase or decrease. In this study 36 of the dogs had a decrease in infestation.
Rcode:
# CI for proportion
p=36/50 ;p
var =p*(1-p)/50 ; var
se =sqrt(var);se
E=qnorm(.975)*se ; E
p+c(-E,E)
# using test of significance
prop.test(36,50,p=0.5,conf.level=.95,alternative = c("less"))
Estimate the probability a dog will have a decrease in infestation and give its 95% confidence limits. Show your work.
# CI for proportion
> p=36/50 ;p
[1] 0.72
> var =p*(1-p)/50 ; var
[1] 0.004032
> se =sqrt(var);se
[1] 0.06349803
> E=qnorm(.975)*se ; E
[1] 0.1244539
> p+c(-E,E)
[1] 0.5955461 0.8444539
95% CI = (0.5955, 0.8445
B. Assume that if there is no effect of the yeast supplement one expects half the dogs to increase and half to decrease. Use a statistical test to determine if the yeast additive is effective in reducing flea infestation. Show your work and give the p-value.
H_0: P = 0.5 H_1: P < 0.5
Lower tail test
prop.test(36,50,p=0.5,conf.level=.95,alternative = c("less"))
1-sample proportions test with continuity correction
data: 36 out of 50, null probability 0.5
X-squared = 8.82, df = 1, p-value = 0.9985
alternative hypothesis: true p is less than 0.5
95 percent confidence interval:
0.000000 0.819471
sample estimates:
p
0.72
Calculated chi square= 8.82, P=0.9985.
There is no evidence to conclude that the yeast additive is effective in reducing flea infestation.
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