Normal Distributions and the Central Limit Theorem

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What is the primary purpose of a null hypothesis in hypothesis testing?

To provide an alternative explanation to the research hypothesis

To serve as a baseline for comparison with the alternative hypothesis (correct)

To ensure the research hypothesis is true

To prove a researcher's claim

What is the definition of a Type 1 error in hypothesis testing?

Shutting down a restaurant that was fine (correct)

Not shutting down a restaurant that should be shut down

Failing to reject a true null hypothesis

Rejecting a false null hypothesis

What is the purpose of statistical inference in linear regression?

To predict the value of y given a value of x

To calculate the correlation coefficient

To draw a conclusion about the population from a sample of data (correct)

To create a scatter plot of the data

What is the definition of a parameter in statistics?

A number associated with a population (B) Signup and view all the answers

What is the purpose of the p-value in hypothesis testing?

To determine the odds of the observed result occurring if the null hypothesis is true (D) Signup and view all the answers

What is the purpose of estimating the parameter of interest with an expression of uncertainty?

To provide an interval estimate of a population parameter (A) Signup and view all the answers

What is the conclusion if the p-value is less than the significance level in a hypothesis test?

We reject the null hypothesis (B) Signup and view all the answers

What is the term for the percentage of variation in the dependent variable that is explained by the independent variable in linear regression?

R-squared (C) Signup and view all the answers

What is the purpose of bootstrapping in the context of parameter estimation?

To simulate the distribution of a test statistic (C) Signup and view all the answers

What is the assumption required for the central limit theorem to hold?

The sample size must be large (B) Signup and view all the answers

What is the purpose of calculating the standard error in the context of parameter estimation?

To quantify the variability of the sample statistic (B) Signup and view all the answers

What is the conclusion if the sample proportion of UPS students who drink coffee is significantly different from the national average?

We reject the null hypothesis that the sample proportion is equal to the national average (A) Signup and view all the answers

What is the purpose of the central limit theorem in the context of statistical inference?

To describe the distribution of a sample mean as the sample size increases (B) Signup and view all the answers

A researcher wants to estimate the average length of a possum's head in a population. If the sample mean is 92.6 and the sample standard deviation is 3.6, what is the standard error of the sample mean?

2.8 (B) Signup and view all the answers

In a hypothesis test, what does the null hypothesis Ho: Pc = Pt represent?

The vaccine has no effect on the infection rate (D) Signup and view all the answers

What is the z-score of a SAT score of 1310, given a mean of 1060 and a standard deviation of 195?

1.28 (B) Signup and view all the answers

According to the 68-95-99.7 rule, what percentage of observations are within two standard deviations of the mean?

95% (B) Signup and view all the answers

What is the purpose of the standard normal distribution in statistical analysis?

To help us talk about other distributions based on z-scores (B) Signup and view all the answers