The manager of a mobile phone provider wishes to know the average length of a ce
ID: 3223147 • Letter: T
Question
The manager of a mobile phone provider wishes to know the average length of a cell phone call for the population of phone calls made by their customers. A random sample of 100 calls is collected. The sample mean is found to be 3.4 minutes and the population standard deviation is known to be 1.2 minutes.
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Identify: X = _____min. = _____min. n = _____
Identify the critical Z or t values for a 95% confidence interval. ____________________________
List the formula for a confidence interval to estimate the mean of the population.
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Use a 95% confidence interval to estimate the mean phone call length for the population of phone calls made by the customers.
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Explanation / Answer
a.
Z - value = 1.96
b.
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
c.
Mean(x)=3.4
Standard deviation( sd )=1.2
Sample Size(n)=100
Confidence Interval = [ 3.4 ± Z a/2 ( 1.2/ Sqrt ( 100) ) ]
= [ 3.4 - 1.96 * (0.12) , 3.4 + 1.96 * (0.12) ]
= [ 3.16,3.64 ]
Interpretations:
1) We are 95% sure that the interval [3.16 , 3.64 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population mean
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