The grammar-corrected and more concise version of the text is: "A magazine article claims that the average weight of one-year-old boys is the same as that for one-year-old girls. Does the confidence interval contradict this claim?"

Mathematics · College · Thu Feb 04 2021

Answered on

To determine if the confidence interval contradicts the claim that the average weight of one-year-old boys is the same as that for one-year-old girls, you would perform the following steps:

1. Gather Data: Obtain a sample of weights for both one-year-old boys and one-year-old girls. Ensure that the sample size is adequate to represent the population.

2. Calculate the Mean Weights: Compute the average (mean) weight for the sample of one-year-old boys and the same for one-year-old girls.

3. Determine the Standard Deviation and Standard Error: Calculate the standard deviation for both samples, which measures the dispersion of the weight data. Then, calculate the standard error, which helps in estimating the precision with which the sample mean represents the population mean.

4. Construct the Confidence Interval: Use the standard error and the mean to construct a confidence interval for the difference in means (boys - girls). The confidence interval will provide a range of values within which the true difference in the population means is likely to fall. A common level of confidence used is 95%.

5.Interpret the Confidence Interval: Examine the confidence interval for the difference in means. If the interval includes zero, the data does not provide strong evidence against the claim, since zero difference means that the averages could be the same. If the interval does not include zero, it suggests that there is a significant difference between the average weights of one-year-old boys and girls, and this would contradict the claim.

Related Questions