Question

A business researcher wants to estimate the average travel time to work in Cleveland. A random sample of 45 Cleveland commuters is taken and the travel time (in minutes) to work is obtained from each. The data is shown in the table below.

27	25	19	21	24	27	29	34	18	29	16	28	20	32	27
28	22	20	14	15	29	28	29	33	16	29	28	28	27	23
27	20	27	25	21	18	26	14	23	27	27	21	25	28	30

1. Define the random variable X in words ________________________________________________
2. Calculate                      X   =     ___________ _Answer
3. Calculate                      sx =     ___________ _Answer
4. You wish to construct a 95% confidence interval for the population mean Cleveland commute time.
   1. Should you use a t-distribution or a z-normal distribution for this confidence interval?

                                                                      ____________________________ _Answer

2. Construct a 90% confidence interval for the population mean commute time.

                                                                                                                                                                                                                                    __________ <   µ   <   _________ _Answer

Answer 1

Part a

The random variable x is the travel time to work in Cleveland.

Part b

From given data, we have

Sample mean = Xbar = 24.5333

[By using excel or calculator]

Part c

Sample standard deviation = S = 5.1239

[By using excel or calculator]

Part d

95% Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 24.5333

S = 5.1239

n = 45

df = n – 1 = 44

Confidence level = 95%

Critical t value = 2.0154

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 24.5333 ± 2.0154*5.1239/sqrt(45)

Confidence interval = 24.5333 ± 1.5394

Lower limit = 24.5333 - 1.5394 = 22.99

Upper limit = 24.5333 + 1.5394 = 26.07

Confidence interval = (22.99, 26.07)

22.99 <   µ   < 26.07

90% Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 24.5333

S = 5.1239

n = 45

df = n – 1 = 44

Confidence level = 90%

Critical t value = 1.6802

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 24.5333 ± 1.6802*5.1239/sqrt(45)

Confidence interval = 24.5333 ± 1.2834

Lower limit = 24.5333 - 1.2834 = 23.25

Upper limit = 24.5333 + 1.2834 = 25.82

Confidence interval = (23.25, 25.82)

23.25 <   µ   < 25.82