Statistical Inference

What is the primary purpose of hypothesis testing?

Hypothesis testing is only relevant when comparing two groups.

What are the two types of hypotheses formulated in hypothesis testing?

A ______ hypothesis test examines the equality of parameters from two different populations.

Match the following scenarios with the appropriate type of hypothesis test:

In the one-sample barista example, the null hypothesis would be that the barista pours ______ ounces of coffee on average.

Hypotheses should be formulated before observing any data.

Give an example of a real-world scenario where a two-sample hypothesis test could be used.

What is the main purpose of statistical inference?

Confidence intervals are used to estimate population quantities using sample data.

What is a sample in the context of statistics?

Statistical inference allows us to make conclusions based on a randomly-selected _______.

Match the following terms with their descriptions:

Why is sampling considered a practical technique in statistics?

It is always necessary to collect data from the entire population to make conclusions.

What example is used to explain sampling in the context of GPA?

What can be concluded if the data indicate to reject the null hypothesis 𝐻𝑜?

You can conclude that the null hypothesis is true based on the sample data.

In the jury system analogy, what is assumed about the defendant?

A jury can only _______ the null hypothesis that the defendant is innocent.

What does failing to reject the null hypothesis indicate?

Match the components of hypothesis testing with their definitions:

What is a challenging part of hypothesis testing?

The jury can conclude that the defendant is guilty if the evidence is strong.

What do we say when the sample data does not provide sufficient evidence to reject the null hypothesis?

Type II errors occur when we incorrectly reject a null hypothesis that is actually true.

What are the two types of hypotheses defined in hypothesis testing?

A one-sample hypothesis test is used to compare a population parameter to a __________ value.

Match the following scenarios with the type of testing they would require:

Which hypothesis test would be appropriate for determining if the true proportion of defective bulbs is less than 0.02?

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

A one-sample hypothesis test can be used to compare both population means and proportions.

What is the null hypothesis when conducting an independent samples t-test?

The alternative hypothesis for a right-sided t-test indicates that the mean of group 1 is less than the mean of group 2.

What is one reason for performing an independent samples t-test?

The null hypothesis for the independent samples t-test is represented as 𝐻𝑜 : 𝜇1 = _____ .

Which of the following scenarios is appropriate for using an independent samples t-test?

Match the following types of alternative hypotheses with their descriptions:

List one possible alternative hypothesis in an independent samples t-test.

In an independent samples t-test, the mean years of schooling of Republicans could be tested against that of Democrats.

What is the purpose of calculating the standard deviation from a sample?

The value of $t^*$ does not depend on the sample size.

What formula is used to calculate the standard deviation from a sample?

For a confidence interval, the degrees of freedom is equal to the sample size (n) minus ______.

Match the following terms to their definitions:

What is the approximate $t^*$ value for a 95% confidence interval with 99 degrees of freedom?

Statistical software may be used to calculate the $t^*$ value instead of looking it up manually.

Which software is mentioned as capable of calculating confidence intervals?