7. Sampling Distributions & Confidence Intervals: Mean

Which of the following is not necessary to determine how large a sample to select from a population when constructing a confidence interval?

In interval estimation, as the sample size $n$ becomes larger, the interval estimate:

In the context of constructing confidence intervals, how does decreasing the confidence level (for example, from $99\%$ to $95\%$) affect the sample size required to achieve a fixed margin of error?

$$Which of the following is not a time-series model?$$

Suppose a random sample of size $n=36$ is taken from a population with unknown mean and known standard deviation $\sigma =12$. The sample mean is $\overline{x}=50$. Calculate the standard error of the mean (rounded to 4 decimal places). May normality be assumed for the sampling distribution of the mean?

If your p-value is $0.11$, what can you conclude at the $0.05$ significance level?

Assuming a $90\%$ confidence level for a population mean with known standard deviation, the margin of error is approximately equal to the critical value times the standard error. Which of the following best represents the margin of error formula for this scenario?

Which of the following must be true for an estimator of a population parameter to be unbiased?

Given the following table showing sample means and confidence intervals for the average test scores of two groups, Group A: sample mean = $75$, 95% confidence interval = $[72,78]$; Group B: sample mean = $80$, 95% confidence interval = $[77,83]$. Which statement is best supported by the data?

In the context of constructing confidence intervals, when is a linear model generally not a good fit for a set of data?

What is the primary purpose of calculating a $confidence interval$ in statistics?

Which of the following is not a conclusion of the central limit theorem?

Given a confidence interval for a population mean, how can you find the point estimate of the mean from the interval endpoints $a$ and $b$?

Based on the statistical model you developed, which of the following best describes a confidence interval for the population mean when the population standard deviation is unknown and the sample size is small?