STATISTICS QUESTION : For this problem, a random sample of 50 passengers between
ID: 3128089 • Letter: S
Question
STATISTICS QUESTION: For this problem, a random sample of 50 passengers between the two airports flying by ZYX
Airlines yielded a mean fare of $165. The population standard deviation of the fare is known
to be $50.
a) Please develop a 94% confidence interval estimate on the fare between the two airports for
ZYX.
b) Develop a 98% confidence interval estimate on the fare between the two airports for
ZYX.
c) Please consider and develop the Hypothesis to answer the question “Is the mean fare between the two
airports on ZYX Airlines different than $145?"
d) Please conduct the hypothesis test using the confidence Interval from section B. What would be your
decision on the hypothesis stated in section C above.
e) What is your conclusion based on the decision from section D?
Explanation / Answer
a)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.03
X = sample mean = 165
z(alpha/2) = critical z for the confidence interval = 1.880793608
s = sample standard deviation = 50
n = sample size = 50
Thus,
Margin of Error E = 13.29921914
Lower bound = 151.7007809
Upper bound = 178.2992191
Thus, the confidence interval is
( 151.7007809 , 178.2992191 ) [ANSWER]
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b)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.01
X = sample mean = 165
z(alpha/2) = critical z for the confidence interval = 2.326347874
s = sample standard deviation = 50
n = sample size = 50
Thus,
Margin of Error E = 16.44976357
Lower bound = 148.5502364
Upper bound = 181.4497636
Thus, the confidence interval is
( 148.5502364 , 181.4497636 ) [ANSWER]
*********************
c)
Ho: u = 145
Ha: u =/= 145
********************
d)
We reject the null hypothesis, because the interval b) do not contain 145 at all.
********************
e)
At 98% confidence, there is significant evidence that the true mean fare between the two airports on ZYX Airlines different than $145.
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