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Suppose you calculate a 95% confidence interval for the mean weight of apples in a batch as (150, 170) grams. You then repeat the experiment with a larger sample size but with the same sample mean and standard deviation. Which of the following statements is correct about the new confidence interval?

The expectation of the difference of two independent random variables is equal to the difference of their expectations, but the variance of the difference is equal to the sum of their variances. 

A researcher calculates the margin of error for a 95% confidence interval for the mean height of a plant species. The sample mean is 20 cm, the sample standard deviation is 4 cm, and the sample size is 16. Using the T-distribution, what is the margin of error of the confidence interval? Choose the best/closest answer. 

An estimated 95% confidence interval for the mean (from a specific, single random sample of size n) implies that there is a 95% probability that the population mean lies within the calculated interval.

A researcher wants to calculate a two-sided 95% confidence interval for the mean time it takes to complete a task. In one study, they take a small sample (n=12) with a sample mean of 30 minutes and a sample standard deviation of 5. In another study, they take a large sample (n=100) with the same sample mean and standard deviation. Which of the following correctly describes the difference between the two confidence intervals?

The concept of historic trauma is distinctive in its exploration of:

If X1,X2,…,XnX_1, X_2, \dots, X_n​ are i.i.d. random variables from a normal distribution with mean μ\mu and variance σ2\sigma^2, the sampling distribution of the sample mean Xˉ\bar{X} has the same variance σ2\sigma^2 regardless of the sample size nn.

What is the probability that some random passenger orders a small cup? 

How would you interpret the probability in the previous question?  This is the [cond] probability that a person purchases [type], given that they ordered a [size].

A point estimator with a smaller variance is always more accurate than an estimator with a larger variance, regardless of sample size.