In: Statistics and Probability
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
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