Question

The director of a customer service center wants to estimate the mean number of customer calls the center handles each day, so he randomly samples 26 different days and records the number of calls. the sample yields a mean of 258.4 calls with a standard deviation of 32.7 calls per day. the 95% confidence interval for the mean number of calls per day has an upper bound of ________. (round your answer to 1 decimal place.)

Answer 1

We can compute for the interval of sample size <30 using the formula:

Confidence Interval = X ± t * S / sqrt(N)

Where it is given that:

X = sample mean = 258.4

t = t-score (taken from standard distribution tables)

S = standard deviation = 32.7

N = sample size = 26

 

From the tables, t = 2.060 (at DF = N -1 =26 and 95% Confidence level)

Calculating for the interval:

95% confidence interval = 258.4 ± 2.060 * 32.7 / sqrt (26)

95% confidence interval = 258.4 ± 13.21 = 271.61 , 245.19

 

ANSWER: Therefore the upper bound is 271.6 calls.