Question

In: Statistics and Probability

The level of carbon monoxide air pollution in parts per million (ppm) is measured at an...

The level of carbon monoxide air pollution in parts per million (ppm) is measured at an entrance ramp to interstate highway I-80 near Iowa City each day. Measurements from two different samples are summarized as follows:

Sample 1: n = 96 x¯ = 126.8 s = 140.2

Sample 2: n = 143 x¯ = 126.8 s = 140.2

Let µ = mean daily level of carbon monoxide pollution at the entrance ramp, in ppm •

Interval 1 is a 90% confidence interval for µ calculated from Sample 1.

Interval 2 is a 99% confidence interval for µ calculated from Sample 1.

Interval 3 is a 99% confidence interval for µ calculated from Sample 2.

4. Calculate Interval 1.

(a) (89.04, 164.56)

(b) (89.19, 164.41)

(c) (102.99, 150.61)

(d) (103.03, 150.57)

(e) (103.26, 150.34)

5. Calculate Interval 2.

(a) (89.04, 164.56)

(b) (89.19, 164.41)

(c) (102.99, 150.61)

(d) (103.03, 150.57)

(e) (103.26, 150.34)

6. Calculate Interval 3.

(a) (89.22, 164.38)

(b) (89.44, 164.16)

(c) (103.05, 150.55)

(d) (107.34, 146.26)

(e) None of the answers is correct to the second decimal place

Solutions

Expert Solution

4.

90% confidence interval for µ calculated from Sample 1.

Standard error = s / = 140.2 / = 14.3091

Degree of freedom = n-1 = 96-1 = 95

Critical value of t at 90% confidence interval and df = 95 is 1.661

90% confidence interval is,

(126.8 - 1.661 * 14.3091,  126.8 + 1.661 * 14.3091)

(103.03 , 150.57)

(d) (103.03, 150.57)

5.

99% confidence interval for µ calculated from Sample 1.

Critical value of t at 99% confidence interval and df = 95 is 2.629

99% confidence interval is,

(126.8 - 2.629 * 14.3091,  126.8 + 2.629 * 14.3091)

(89.18 , 164.42)

(b) (89.19, 164.41)

6.

99% confidence interval for µ calculated from Sample 2.

Standard error = s / = 140.2 / = 11.72411

Degree of freedom = n-1 = 143-1 = 142

Critical value of t at 99% confidence interval and df = 142 is 2.611

99% confidence interval is,

(126.8 - 2.611 * 11.72411,  126.8 + 2.611 * 11.72411)

(96.19 , 157.41)

(e) None of the answers is correct to the second decimal place


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