Question 19 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A government agency constructs a 95% confidence interval to estimate the mean amount of pollution in a city’s river. Assume that all conditions have been met. The one-sample t-interval is (1.26, 3.91).
Answer
A
No. Because 4.00 is close to the upper bound of the interval, it is reasonable to believe the river is not contaminated.
B
No. Because the interval representing the mean amount of pollution is entirely below 4.00, it is reasonable to believe the river is not contaminated.
C
Yes. Because 4.00 is close to the upper bound of the interval, it is reasonable to believe the river is contaminated.
D
Yes. Because the interval representing the mean amount of pollution is entirely below 4.00, it is reasonable to believe the water is contaminated.
Explanation
The 95% confidence interval for the mean pollution level is from 1.26 to 3.91. Since the entire interval is below the contamination threshold of 4.00, the data support the conclusion that the river is not contaminated. Choice B states this correctly; being close to the threshold does not make the interval include or exceed it.
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