Kate and Leopold are thinking about buying the Rockwood motel located interstate
ID: 3157559 • Letter: K
Question
Kate and Leopold are thinking about buying the Rockwood motel located interstate 70. Before they make up their mind, they want to estimate the average number of vehicles that go by the motel each day in the summer. Fortunately, the highway department has been counting vehicles on I 70 near the motel. A random sample of 36 summer days show a mean of 16,000 cars per day with the standard deviation of 2400 cars. find a 75% confidence interval for the population mean number of cars per summer day going past the Rockwood motel. Verbalize your result! Show formula used.
Explanation / Answer
Note that
Margin of Error E = t(alpha/2) * s / sqrt(n)
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.125
X = sample mean = 16000
t(alpha/2) = critical t for the confidence interval = 1.169764906
s = sample standard deviation = 2400
n = sample size = 36
df = n - 1 = 35
Thus,
Margin of Error E = 467.9059626
Lower bound = 15532.09404
Upper bound = 16467.90596
Thus, the confidence interval is
( 15532.09404 , 16467.90596 ) [ANSWER]
**************************
Hence, we are 75% confident that the true mean number of cars per summer day going past the Rockwood motel is between 15532.09404 and 16467.90596. [CONCLUSION]
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.