Thomari constructs a 95% confidence interval to estimate the proportion of students at her high school who like the cafeteria food. Assume that all conditions have been met. Her 95% one-proportion z-interval is (0.23, 0.46).Is it reasonable to conclude that the majority of the students at Thomari’s high school do not like the cafeteria food?
Answer
A
Yes, because the interval of students who like the food does not contain 0.5, the interval of students who do not like the food would be entirely below 0.5.
B
Yes, because the interval of students who like the food is entirely below 0.5, the interval of students who do not like the food would be entirely above 0.5.
C
No, because a different sample might give different results, so no conclusion can be drawn.
D
No, because Thomari’s interval is entirely below 0.5, so it cannot represent a majority.
Explanation
The interval estimates the proportion who like the food as 0.23 to 0.46, entirely below 0.50. The proportion who do not like it is the complement, so its interval is 1 − 0.46 to 1 − 0.23, or 0.54 to 0.77. Since this entire interval is above 0.50, it is reasonable to conclude that a majority do not like the food.
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