7. Sampling Distributions & Confidence Intervals: Mean

Which of the following is a point estimate?

Suppose a 95% confidence interval for the mean difference in blood pressure between a treatment group and a control group is $(-2,5)$. What does this confidence interval suggest about the effectiveness of the treatment?

Which of the following best describes a $95\%$ confidence interval for a population mean?

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

Finding Probabilities In Exercises 15–18, the population mean and standard deviation are given. Find the indicated probability and determine whether the given sample mean would be considered unusual.

For a random sample of n=36, find the probability of a sample mean being less than 12,750 or greater than 12,753 when mu=12750 and 1.7.

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?

Bachelor’s Degree The president of Brown University wants to estimate the mean time (years) it takes students to earn a bachelor’s degree. How many students must be surveyed in order to be 95% confident that the estimate is within 0.2 year of the true population mean? Assume that the population standard deviation is sigma=1.3 years

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?