A random sample of 28 parking meters in a large municipality produced the follow
ID: 3182037 • Letter: A
Question
A random sample of 28 parking meters in a large municipality produced the following daily incomes:
$2.60 $1.05 $2.45 $2.90 $1.00 $4.52 $8.80
$1.30 $3.10 $2.35 $2.00 $2.75 $10.50 $0.75
$2.40 $2.35 $2.40 $1.95 $1.80 $16.35 $4.50
$2.80 $2.50 $2.10 $1.75 $1.95 $3.45 $6.65
Determine a 90% confidence interval for the true mean daily income of parking meters in this municipality, assuming that the daily incomes follow a normal distribution and then, interpret this interval. Be sure to use the flowchart in section 6.2 in order to determine if the z distribution or the t distribution is appropriate.
PLEASE TYPE THE ANSWER!!
Explanation / Answer
Solution
Back-up Theory
Let X = Daily income of the parking meters. We are given X ~ N(µ, 2).
100(1 – ) % confidence interval for µ when 2 is unknown is: {Xbar ± (s/n)(t/2)}, where
Xbar = sample mean,
= population standard deviation,
s = sample standard deviation,
n = sample size and
t/2 = upper (/2) % point of t-Distribution with (n - 1) degrees of freedom..
Now, to work out solution,
Given, n = 28, = 0.05,
From the given data, computation yields: Xbar = 3.535, s = 3.352, and using Excel Function ,
t/2 = t27, 0.05 = 1.703
90% Confidence Interval for µ is: {3.535 ± (3.352/28)(1.703)} = (3.535 ± 1.073)
Lower Bound = 2.462, Upper Bound = 4.608 ANSWER
Since 2 is unknown, its estimate, sample standard deviation is used and hence the appropriate distribution is t and NOT Z.
Interpretation
The mean daily income from parking meters is expected to be within 2.462 to 4.608 with 90% confidence. Or, in other words, there is only 10% chance that the daily income from parking meters will be less than 2.462 or more than 4.608.
DONE
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