7. Sampling Distributions & Confidence Intervals: Mean

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

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?

Which of the following best describes the interpretation of a $95\%$ confidence interval for the difference in means when conducting an ANOVA comparing three treatment conditions?

When constructing a 93% confidence interval for a population proportion $p$, what value of $z$ should be used as the critical value?

Which of the following best describes how a confidence interval for the difference in treatment means ($\mu \_1-\mu \_2$) is used in statistical inference?

Suppose a chart shows that a $95\%$ confidence interval for the mean height of a population is $(65,70)$ inches. Which explanation is best supported by these numbers?