Question

Listed below are speeds (mi/hr) measured from the Southbound traffic on I-280 freeway. The speed limit for this road is 65 mph.

62 61 61 57 61 54 59 58 59 69 60 67

a) Construct a 95 confidence interval given that the population standard deviation is unknown

b) Explain what will happen to the length of the confidence interval if we increased the sample size

c) Explain what will happen to the margin of error if we decrease the sample size

Answer 1

a) Construct a 95 confidence interval given that the population standard deviation is unknown

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 60.66666667

S = 4.075053448

n = 12

df = n – 1 = 11

Confidence level = 95%

Critical t value = 2.2010

(by using t-table)

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

Confidence interval = 60.66666667 ± 2.2010*4.075053448/sqrt(12)

Confidence interval = 60.66666667 ± 2.5892

Lower limit = 60.66666667 - 2.5892 = 58.07747

Upper limit = 60.66666667 + 2.5892 = 63.25587

Confidence interval = (58.07747, 63.25587)

b) Explain what will happen to the length of the confidence interval if we increased the sample size

If we increase the sample size, then the length of the confidence interval will be decrease by assuming all other factors constant.

c) Explain what will happen to the margin of error if we decrease the sample size.

If we decrease the sample size, then the margin of error of the confidence interval will be increase by assuming all other factors constant.