Inference Review Checkpoint

A 95% CI for mu is (42.1, 49.7). You test H0: mu = 50 at alpha = 0.05 (two-sided). What do you conclude?

You run t.test(x, mu = 100, alternative = 'less') and get p-value = 0.031 with alpha = 0.05. What is the correct conclusion?

A sample of n = 36 has x-bar = 84 and s = 12. What is the standard error of the mean?

For t.test(x, mu = 50), what are the degrees of freedom if length(x) = 20?

In a two-sample t-test for H0: p1 = p2, which standard error formula do you use?

You have before/after measurements on the same 15 subjects. Which test should you use?

What is the default value of var.equal in R's t.test() function?

A linear model gives b1 = 3.2 with SE(b1) = 0.8 and n = 22. What is the t-statistic for testing H0: beta1 = 0?

In regression, a prediction interval (interval='prediction') is ______ a confidence interval (interval='confidence') at the same x.

A residual plot shows a clear U-shaped (curved) pattern. Which regression assumption is violated?

Two groups: n1 = 30, s1 = 5; n2 = 30, s2 = 5. Which test is more appropriate?

For a one-sample t-test with n = 24, the degrees of freedom is ___.

The formula for the standard error of a sample mean is ___. (Write in the form s/sqrt(n))

Which of the following are true about Welch's t-test? Select ALL that apply.

A 95% CI for (mu1 - mu2) is (1.2, 8.4). Select ALL correct conclusions.

A 95% CI for mu is (12.3, 18.7). Which interpretation is correct?

What happens to CI width as sample size n increases?

You get a p-value of 0.03 with alpha = 0.05. What is your conclusion?

What is a Type I error?

In R, t.test(x, mu = 10) tests:

In a two-group proportion study, H0: p1 = p2. For the hypothesis test SE, should you use pooled or individual proportions?

SE of p-hat when p-hat = 0.6, n = 100?

For a 95% CI for a proportion, which z* value?

For two proportions, if the 95% CI for (p1 - p2) is (-0.05, 0.15), what can you conclude?

When comparing two proportions, why use the pooled proportion in the hypothesis test but individual proportions for the CI?

A researcher selects a random sample of 50 students and measures their study time per week. The sample mean is 12.5 hours and the sample standard deviation is 3.2 hours. Which distribution should be used to construct a confidence interval for the population mean?

For a sample of n = 100 from a population, the sample mean is 45 and the sample standard deviation is 8. The 95% confidence interval for the population mean is closest to which of the following? (Assume t* is approximately 1.984 for df = 99)

What does the standard error (SE) measure?

For a hypothesis test with H0: mu = 100 and Ha: mu not equal to 100, the computed test statistic is t = 2.5 with df = 40. The p-value should be calculated as:

You calculate a 95% confidence interval for a population mean: [22.3, 28.7]. If you test H0: mu = 30 vs Ha: mu != 30 at the 0.05 significance level using the same data, what should you conclude?

When we use the t-distribution instead of the z-distribution for inference about a mean, we do so because:

A study reports a p-value of 0.03 for a hypothesis test with alpha = 0.05. Which statement is correct?

In which situation should you use a paired t-test rather than an independent samples t-test?

In the pooled standard deviation formula s_p = sqrt(((n1-1)s1^2 + (n2-1)s2^2) / (n1+n2-2)), what role do the terms (n1-1) and (n2-1) play?

Which statement is correct about Welch's t-test compared to the standard equal-variance t-test?

What are the degrees of freedom for an equal-variance two-sample t-test with n1=30 and n2=28?

When conducting a paired t-test, what is the first calculation you must perform on your data?

A 95% confidence interval for the difference in means is calculated as [1.2, 4.8]. What can you conclude about the null hypothesis that mu1 = mu2 at the 0.05 significance level?

In R's t.test() function, what does the parameter var.equal=TRUE versus var.equal=FALSE specify?

A correlation of r = -0.8 between two variables means:

If R-squared = 0.81 for a regression model, what does this tell us?

In a regression model predicting height (inches) from age (months), the slope is estimated as b1 = 0.35. How should we interpret this?

You create a residual plot for your regression model and observe a curved pattern (upward then downward). Which assumption is violated?

When conducting a hypothesis test for the slope in regression with n = 25 observations, what are the degrees of freedom?

Why is a prediction interval (PI) always wider than a confidence interval (CI) for the same x value?

A regression model has b0 = 5 and b1 = 3. What is the predicted value when x = 4?