hey The university is interested in the mean number of younger siblings a studen

Question

hey The university is interested in the mean number of younger siblings a student has at the university (in the hope that they will attended the university). They randomly sample three students and ask them how many siblings they have, they answer 0,1,3. The sample mean is 1.33 and the sample standard deviation is 1.53. They use this information to construct a 90% confidence interval (using the t-distribution) for the mean number of students | 1.33-2.92×--, 1.33 + 2.92× It is worth noting that the sample mean 1.33 is a number drawn from the bottom plot, which is the distribution of the average [-1.35,4.01] . A rough plot for the distribution of the number of siblings is given in the image below ts worth noting thut the sanserets 9x.1 33 Sampling Distributions 1 time5 times 1000 times Reset | Info Population Mean Median Unadjusted Std. dev Siblings Samples Sample size Mean Median Std. dev 6000 5000 4000 3000 2000 1000 Sample means #of Samples Mean Median Std. dev Sample means

Explanation / Answer

The correct answer for this would be C- Even though it is clear that the sample mean is not normally distributed, by using t-distribution to construct the confidence interval we have correct for the lack of normality of the data

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