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In a study of 40 randomly selected captive Octopus vulgaris, researchers found that the octopuses could learn to integrate visual and tactile information to find food after a mean of 119 trials. The estimate had a margin of error of 18 trials at a
95% confidence level. Which of the following is the most reasonable conclusion about the number of trials it would take all captive Octopus vulgaris in general to learn to find the food?
Choose 1 answer:
(A) The evidence suggests that half of them would require 119 or fewer trials.
(B) The evidence suggests that the mean number of trials would be 119 trials.
(C) The evidence suggests that the mean number of trials would be between 119 and 137 trials.
(D) The evidence suggests that the mean number of trials would be between 101 and 137 trials.

In a study of $40$ randomly selected captive Octopus vulgaris, researchers found that the octopuses could learn to integrate visual and tactile information to find food after a mean of $119$ trials. The estimate had a margin of error of $18$ trials at a $95 \%$ confidence level. Which of the following is the most reasonable conclusion about the number of trials it would take all captive Octopus vulgaris in general to learn to find the food? $\newline$ Choose $1$ answer: $\newline$ (A) The evidence suggests that half of them would require $119$ or fewer trials. $\newline$ (B) The evidence suggests that the mean number of trials would be $119$ trials. $\newline$ (C) The evidence suggests that the mean number of trials would be between $119$ and $137$ trials. $\newline$ (D) The evidence suggests that the mean number of trials would be between $101$ and $137$ trials.

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Interpret confidence intervals for population means

Full solution

Q. In a study of

40

randomly selected captive Octopus vulgaris, researchers found that the octopuses could learn to integrate visual and tactile information to find food after a mean of

119

trials. The estimate had a margin of error of

18

trials at a

95 \%

confidence level. Which of the following is the most reasonable conclusion about the number of trials it would take all captive Octopus vulgaris in general to learn to find the food?

\newline

Choose

1

answer:

\newline

(A) The evidence suggests that half of them would require

119

or fewer trials.

\newline

(B) The evidence suggests that the mean number of trials would be

119

trials.

\newline

(C) The evidence suggests that the mean number of trials would be between

119

and

137

trials.

\newline

(D) The evidence suggests that the mean number of trials would be between

101

and

137

trials.

Margin of Error Calculation: The margin of error is $18$ trials, which means the true mean could be $18$ trials more or less than the observed mean of $119$ trials.
Lower Limit Calculation: Calculate the lower limit of the confidence interval: $119$ trials - $18$ trials = $101$ trials.
Upper Limit Calculation: Calculate the upper limit of the confidence interval: $119$ trials + $18$ trials = $137$ trials.
Reasonable Conclusion: The most reasonable conclusion is that the mean number of trials for all captive Octopus vulgaris to learn to find food would be between the lower and upper limits of the confidence interval.

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