QUESTION 1: You have been hired to estimate the proportion of Pennsylvanian adul
ID: 2921976 • Letter: Q
Question
QUESTION 1:You have been hired to estimate the proportion of Pennsylvanian adults who are fans of the Philadelphia Eagles. You survey a random sample of 216 Pennsylvanian adults. Of these, 68 are Philadelphia Eagles fans.
PART A: What is your best point estimate for the proportion of Pennsylvanian adults who are Philadelphia Eagles fans? (Express your answer as a decimal rounded to four decimal places.)
PART B:Create a 99% CI for the proportion of Pennsylvanian adults who are Philadelphia Eagles fans. Express each end of the CI as a decimal rounded to four decimal places.
PART C:The 99% CI is _________
QUESTION 2: A study is done on a sample of 41 adult males. It is determine that the standard deviation of the heights of adult males has a 95% CI of (2.6, 3.9) in.
Look at the following statements and select all of them that are true.
A) 95% of the time, the true population standard deviation of heights of adult males is between 2.6 and 3.9.
B) If many studies on samples of size 41 were performed and a confidence interval were made for each of them, 95% of these confidence intervals would include the true population standard deviation.
C) If many studies were done with a sample of size 41, 95% of them would yield a confidence interval of (2.6, 3.9).
D) 5% of the time the true population standard deviation of heights of adult males would fall outside the range 2.6 to 3.9.
QUESTION 3: You have been hired to estimate the mean of how much water adults drink per day. You obtain a sample of 85 adults. In this sample, the mean amount of water consumed in a day is 893 mL with a standard deviation of 348 mL.
PART A: What is your best point estimate for the mean amount of water being consumed per day by adults? (Include units)
PART B:Create a 95% confidence interval of the mean amount of water being consumed per day by adults. Express your answer rounded to one decimal place. Don't include units this time.
PART C: The 95% CI is___________
QUESTION 4: It is known that the recovery time from an appendectomy surgery is normally distributed. You have been hired to determine the standard deviation of the recovery time from an appendectomy surgery.
You obtain a sample of 72 patients having appendectomy surgery and measure the recovery time of each. The mean recovery time of your sample is 57.3 min with a standard deviation of 13.2 min.
PART A:What is the best point estimate of the standard deviation of the recovery time from an appendectomy surgery? Include units.
PART B:Create a 95% confidence interval for the standard deviation of the recovery time from an appendectomy surgery. Round your answer to two decimal places. This time do not include units.
PART C: The 95% CI is_________
PLEASE COMPLETE ALL 4 QUESTIONS FULLU AND ALL PARTS TO EACH QUESTION FOR FULL RATING!!
Explanation / Answer
Q1.
TRADITIONAL METHOD
given that,
possibile chances (x)=68
sample size(n)=216
success rate ( p )= x/n = 0.315
I.
sample proportion = 0.315
standard error = Sqrt ( (0.315*0.685) /216) )
= 0.032
II.B9
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.01
from standard normal table, two tailed z /2 =2.576
margin of error = 2.576 * 0.032
= 0.081
III.
CI = [ p ± margin of error ]
confidence interval = [0.315 ± 0.081]
= [ 0.233 , 0.396]
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DIRECT METHOD
given that,
possibile chances (x)=68
sample size(n)=216
success rate ( p )= x/n = 0.315
CI = confidence interval
confidence interval = [ 0.315 ± 2.576 * Sqrt ( (0.315*0.685) /216) ) ]
= [0.315 - 2.576 * Sqrt ( (0.315*0.685) /216) , 0.315 + 2.576 * Sqrt ( (0.315*0.685) /216) ]
= [0.233 , 0.396]
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[ANSWERS]
a. best point estimate = 0.315
b. [0.233 , 0.396]
c. interpretations:
1. We are 99% sure that the interval [ 0.233 , 0.396] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 99% of these intervals will contains the true population proportion