Statistics Fundamentals

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Questions and Answers

Which of the following statements best describes the relationship between the standard deviation and the variance?

The standard deviation is the square root of the variance. (correct)
The standard deviation and variance are unrelated measures of dispersion.
The variance is the square root of the standard deviation.
The standard deviation is the square of the variance.

In hypothesis testing, what does the p-value represent?

The probability that the null hypothesis is true.
The probability of observing a test statistic as extreme as, or more extreme than, the one computed if the null hypothesis is true. (correct)
The probability of failing to reject the null hypothesis when it is false.
The probability of rejecting the null hypothesis when it is true.

What is the key difference between a discrete and a continuous probability distribution?

Discrete distributions describe probabilities for countable variables, while continuous distributions describe probabilities for variables that can take any value within a range. (correct)
Discrete distributions are used for small sample sizes, while continuous distributions are used for large sample sizes.
Discrete distributions are symmetric, while continuous distributions are skewed.
Discrete distributions can only take positive values, while continuous distributions can take negative values.

When is it most appropriate to use the t-distribution instead of the standard normal distribution?

When the population standard deviation is unknown and the sample size is small. (B) Signup and view all the answers

What does the Central Limit Theorem state about the sampling distribution of the sample mean?

The sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population distribution. (D) Signup and view all the answers

A researcher wants to estimate the average height of students at a university. They collect a random sample of 50 students and calculate a 95% confidence interval for the mean height. What does the 95% confidence level indicate?

If the researcher repeated the sampling process many times, 95% of the resulting confidence intervals would contain the true population mean. (A) Signup and view all the answers

Which of the following real-world scenarios is best modeled by a Poisson distribution?

The number of cars passing a certain point on a highway in one hour. (D) Signup and view all the answers

In a normal distribution, approximately what percentage of the data falls within two standard deviations of the mean?

95% (B) Signup and view all the answers

What is the purpose of calculating a z-score?

To standardize a value from a normal distribution, allowing for comparison across different distributions. (D) Signup and view all the answers

A researcher conducts a hypothesis test with a significance level of $\alpha = 0.05$. They fail to reject the null hypothesis. What type of error is possible in this scenario?

Type II error (C) Signup and view all the answers

Flashcards

Probability Distribution

A function describing likelihoods of possible values a random variable can assume.

Discrete Probability Distribution

Describes probabilities for discrete random variables.