good stats

If a histogram is skewed right, what is the relationship between the mean and the median?

Mean is greater than median (mean > median)

If a histogram is skewed left, what is the relationship between the mean and the median?

Mean is less than median (mean < median)

Which is more resistant to outliers: mean or median?

Median

What does a boxplot show that a histogram does not?

Exact five-number summary (Min, Q1, Median, Q3, Max) and outliers

Using the IQR method, a value is an outlier if it falls below what?

Q1 - 1.5 × IQR

Using the IQR method, a value is an outlier if it falls above what?

Q3 + 1.5 × IQR

If two events are mutually exclusive, can they be independent?

No, not unless one has probability zero.

What is the difference between mutually exclusive and independent events?

Mutually exclusive means events cannot happen together; independent means one event does not affect the probability of the other.

Does P(A|B) equal P(B|A) in general?

No, only when P(A) equals P(B).

If P(A)=0.5, P(B)=0.5, and P(A∩B)=0.25, are A and B independent?

Yes, because P(A)×P(B)=0.25 which equals P(A∩B).

In a tree diagram, how do you find the probability of reaching a final branch?

Multiply the probabilities along all branches leading to that outcome.

What is the probability of neither A nor B occurring?

1 minus P(A union B), which is 1 minus [P(A)+P(B)-P(A∩B)].

What distribution is used when counting the number of defective items in a sample of 10 drawn without replacement?

Hypergeometric.

What distribution is used when counting the number of customers arriving at a store in one hour?

Poisson.

What distribution is used when flipping a coin 20 times and counting the number of heads?

Binomial.

What distribution is used when flipping a coin until the first head is obtained?

Geometric.

What is a key clue that indicates the use of Poisson distribution instead of Binomial?

No fixed number of trials; counting events over time/area rather than number of attempts.

For any continuous distribution, what is P(X equals an exact value)?

Zero.

What are the mean and standard deviation of the standard normal distribution?

Mean = 0, Standard deviation = 1.

What percentage of data falls within 2 standard deviations of the mean in a Normal distribution?

Approximately 95%.

What percentage of data falls within 1 standard deviation of the mean in a Normal distribution?

Approximately 68%.

What type of real-world phenomenon is often modeled by the exponential distribution?

Waiting times or lifetimes.

As sample size increases, what happens to the sampling distribution of the sample mean?

It becomes more Normal and narrower.

Does the Central Limit Theorem apply to the sample median?

No.

If the population is Normal, what is the shape of the sample mean's distribution for any sample size?

Normal.

What is the standard deviation of the sample mean called?

Standard error.

If sample size increases, does the standard error increase or decrease?

Decrease.

What does unbiased mean in plain English?

On average, the estimator hits the true parameter value.

Is the sample variance s-squared unbiased for the population variance sigma-squared?

Yes.

Is the sample standard deviation s unbiased for the population standard deviation sigma?

No.

What does a consistent estimator mean?

As sample size increases, the estimator gets closer to the true parameter value.

True or false: A 95% confidence interval means there is a 95% probability the parameter is in this specific interval.

False.

If you increase the confidence level from 90% to 99%, what happens to the interval width?

It gets wider.

If you increase the sample size, what happens to the confidence interval width?

It gets narrower.

A 95% confidence interval for the population mean is (10, 20). Does this mean 95% of the data falls between 10 and 20?

No.

What is the difference between margin of error and interval width?

Interval width = 2 × Margin of Error.

In plain English, what is a p-value?

The probability of observing data as extreme as what you got, assuming the null hypothesis is true.

A small p-value provides evidence for or against the null hypothesis?

Against the null hypothesis.

If you fail to reject the null hypothesis, does that mean it's true?

No.

What is a Type I error?

False positive - rejecting the null hypothesis when it is true.

What is a Type II error?

False negative - failing to reject the null hypothesis when it is false.

Which type of error is controlled by the significance level alpha?

Type I error.

Which test should you use for the same subjects measured before and after a treatment?

Paired t-test.

Which test should you use for two separate groups with different subjects?

Two-sample t-test.

For a two-proportion z-test, what is the minimum sample size requirement?

At least 5 successes and 5 failures in each group.

What does a slope of zero indicate about the relationship between X and Y?

There is no linear relationship.

If R-squared equals 0.64, what percentage of variation in Y is explained by X?

64%.

If R-squared equals 0.64 and the slope is positive, what is the correlation r?

0.8.

Which is wider: a confidence interval for the mean response or a prediction interval for a new observation?

Prediction interval.

What does the residual standard error estimate?

Sigma, the typical distance of points from the regression line.

If the slope is positive, what sign does the correlation r have?

Positive.

True or false: "We accept the null hypothesis" is correct statistical wording.

False.

True or false: A 95% confidence interval means 95% of sample means fall in this interval.

False.

True or false: The sample standard deviation s is an unbiased estimator of the population standard deviation sigma.

False.