1. A simple random sample of 120 vet clinics in the Midwest reveals that the vas
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Question
1. A simple random sample of 120 vet clinics in the Midwest reveals that the vast majority of them only treat small pets (dogs, cats, rabbits, etc.) and no large animals (cows, horses, etc.). Of the 120 clinics sampled, 88 responded that they do not treat large animals at their clinic.
a. What is a 90% confidence interval for p, the population proportion of vet clinics that do treat large animals? Tell whether the population proportion of vet clinics that do treat large animals is above 25%. Why? b. If a 95% confidence interval were calculated instead, what would happen to the width of the confidence interval? Why?
2. Ten couples are participating in a small study on cholesterol. Neither the man nor the woman in each couple is known to have any problems with high cholesterol. The cholesterol measurements for the ten couples are given below.
a. The researcher conducting a test wishes to determine if there is evidence that the cholesterol level for the husband tends to be higher than the cholesterol level for the wife.
b. Why do you use the test above for part a?
Couple 1 2 3 4 5 6 7 8 9 10 Husband cholesterol 224 310 266 332 244 178 280 276 242 260 Wife cholesterol 200 270 288 296 270 180 268 244 210 236Explanation / Answer
Q1.
Q1.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=88
Sample Size(n)=120
Sample proportion = x/n =0.733
Confidence Interval = [ 0.733 ±Z a/2 ( Sqrt ( 0.733*0.267) /120)]
= [ 0.733 - 1.645* Sqrt(0.002) , 0.733 + 1.65* Sqrt(0.002) ]
= [ 0.667,0.799]
Interpretations:
1) We are 90% sure that the interval [0.667 , 0.799 ] contains the true population proportion
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion
Tell whether the population proportion of vet clinics that do treat large animals is above 25%. Why?
yes, it is , since the confidence we achived is above 25%
When using 85% confidence the width of the interval is varied
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