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Answer :
To halve the width of a 99% confidence interval, a scientist must increase the sample size by a factor of four. If the initial sample size was 47 hatchlings, the scientist will need to measure 141 additional hatchlings to achieve the journal's requirement. Therefore, the correct answer is option d) 47.
In the context of statistics, a confidence interval provides a range within which we can say with a certain level of confidence that the true parameter of a population lies. The width of the confidence interval is inversely proportional to the square root of the sample size; therefore, to reduce the width of the 99% confidence interval by half, the scientist would have to increase the sample size by a factor of four.
Given the z-value for a 99% confidence interval is 2.576 and the scientist initially measured 47 hatchlings, if they want to achieve a confidence interval half as wide, they need to increase the sample size from 47 to 188 because 47 multiplied by 4 equals 188.
Hence, the scientist would need to measure an additional 141 hatchlings (188 total - 47 already measured) to reach the desired confidence interval width.
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