Final Exam Review

What does filter(df, !is.na(score)) do?

Which ggplot2 geom creates a histogram?

What does group_by(dept) %>% summarize(avg = mean(salary)) return?

pivot_longer() converts data from ______ format to ______ format.

X ~ Binomial(10, 0.3). What R code gives P(X >= 4)?

X ~ N(100, 225) (mean=100, sd=15). What R code gives P(X < 85)?

A population has mean 60 and sd 10. For samples of n=25, the sampling distribution of x-bar has:

What does a p-value of 0.003 mean?

For a single proportion CI, which formula gives the standard error?

A one-sample t-test gives t = 2.5 with df = 15. How do you get the two-sided p-value in R?

You want to test if two independent groups have different means, and their SDs are very different (s1=4, s2=18). Which test?

In the regression model y-hat = 12 + 0.5*x, what does the slope 0.5 mean?

summary(lm(y ~ x)) shows the slope estimate as 2.4 with p-value = 0.002. What null hypothesis was tested?

Which condition is required for the normal approximation to p-hat to be valid?

An inner_join(A, B, by='id') returns:

In R, qt(0.975, df = 19) gives the t* critical value for a ___% confidence interval with n = 20.

The pooled standard deviation formula is: s_p = sqrt(((n1-1)s1^2 + (n2-1)s2^2) / ___). Fill in the denominator.

Which of the following are correct interpretations of a 95% confidence interval (42, 58) for mu? Select ALL that apply.

Which conditions must hold for the normal approximation to p-hat to be valid? Select ALL that apply.

For regression inference, the degrees of freedom for testing the slope is n minus ___.

Consider: rent <- 1200; utilities_adj <- utilities + '10'. Assuming utilities is not defined, what happens when this code runs?

What does class(TRUE) return?

Which of these is an ILLEGAL variable name in R?

Given the starwars dataset (87 rows, 14 columns), what does starwars[1,] return?

What does starwars[,4] return?

What does starwars$hair_color return?

You have the noble gases data with columns Gas and num_isotopes. You want bars showing the number of isotopes for each gas. Which geom should you use?

An airport wants to count the number of flights per carrier from a raw flights dataset. Which geom is best?

In ggplot(mtcars, aes(y = mpg)) + geom_boxplot(aes(fill = as.factor(cyl))), where is fill — global or local? Variable or constant?

You want to find pitchers with at least one shutout game (PIT_SHO > 0). Which filter condition is correct?

You want non-pitcher players with more than 70 double plays AND fewer than 10 errors. Which filter is correct?

You want to add a column metric_value where height (inches) is converted to cm (x 2.54) and weight (lbs) to kg (x 0.45). Which case_when is correct?

A hiring agency wants to interview students whose language fluency data IS available. The Major table has 20 students; Language has 50 students; 15 are in both. Which join gives only the 15 common students?

You want all players from the baseball dataset who have NOT previously won an award (stored in past_awardees). Which join do you use?

The long-format children dataset has 6 rows (3 kids x height/weight). After pivot_wider(names_from = measurement, values_from = value), what is true about wide_data?

If P(A) = 0.3, what is P(A')?

P(A) = 0.4, P(B) = 0.5, P(A and B) = 0.2. What is P(A or B)?

A and B are independent, P(A)=0.3, P(B)=0.4. What is P(A and B)?

What does dbinom(5, 10, 0.5) compute?

X ~ Binomial(15, 0.4). What is E[X]?

How would you compute P(X >= 3) for X ~ Binomial(8, 0.25)?

For X ~ N(50, 9) (mean=50, variance=9), what is the standard deviation?

What does pnorm(1.96) (default mean=0, sd=1) approximately return?

Heights ~ N(68, 9). About what % of people are between 65 and 71 inches?

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:

Why use t-distribution instead of normal for most t-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?

For the normal approximation to be valid for proportions, which condition must hold?

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?

What is the degrees of freedom (df) for a one-sample t-test with n = 85 observations?

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?

When setting up a hypothesis test to compare two population means, which statement describes a correct null and alternative hypothesis pair?

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?

In a hypothesis test for the slope, H0: beta1 = 0 means: