8 Introduction to Hypothesis Testing

Question 1

What is the definition of a STATISTIC?

Answer 1

A numerical property of a sample, which is a function of only values in that sample

It is used in hypothesis testing to assess claims about population parameters.

Question 2

What is the definition of a PARAMETER?

Answer 2

A numerical property of the population

Parameters are often unknown and are estimated using statistics from samples.

Question 3

What are the two hypotheses in hypothesis testing?

Answer 3

• Null Hypothesis (H0)
• Alternative Hypothesis (H1)

Hypotheses are always written about parameters for the population.

Question 4

What is the critical value in hypothesis testing?

Answer 4

The critical value is the value at which the null hypothesis begins to be rejected.

It defines the boundary of the critical region.

Question 5

What is the significance level of a test?

Answer 5

The significance level is the probability of rejecting the null hypothesis.

It defines the critical region for the hypothesis test.

Question 6

True or false: The significance level is always assumed to be 5% if not stated.

Answer 6

TRUE

This is a common convention in hypothesis testing.

Question 7

What are the six steps of a hypothesis test?

Answer 7

• Hypotheses
• Distribution
• Sketch
• Calculation
• Compare and Decide
• Conclusion

These steps guide the process of hypothesis testing.

Question 8

What is the Product Moment Correlation Coefficient (PMCC) used for?

Answer 8

It is used to measure the strength and direction of the linear relationship between two variables.

It is applicable when the underlying data is bivariate normal.

Question 9

What is the Spearman’s Rank Correlation Coefficient (SRCC) used for?

Answer 9

It is used to measure the strength and direction of the association between two ranked variables.

It is applicable when the underlying data cannot be assumed to be bivariate normal.

Question 10

What is the acceptance region in hypothesis testing?

Answer 10

The region where the null hypothesis is not rejected.

It is the complement of the critical region.

Question 11

What is the critical region in hypothesis testing?

Answer 11

The region where the null hypothesis is rejected.

It is determined by the significance level.

Question 12

What is the Binomial Distribution used for?

Answer 12

It is used to test the proportion within a distribution of a particular sample size.

It applies when there are two possible outcomes in a fixed number of trials.

Question 13

What is the P-value in hypothesis testing?

Answer 13

The P-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.

It helps determine the significance of the results.

Question 14

What is the mean in statistics?

Answer 14

The average value of a set of numbers.

It is calculated by summing all values and dividing by the number of values.

Question 15

What is the standard deviation?

Answer 15

A measure of the amount of variation or dispersion in a set of values.

It indicates how much individual data points differ from the mean.

Question 16

What is the standard error?

Answer 16

The standard deviation of the sampling distribution of a statistic.

It provides an estimate of the variability of the sample mean.

Question 17

What is the variance in statistics?

Answer 17

The average of the squared differences from the mean.

It quantifies how much the data points differ from the mean.

Question 18

What does correlation measure?

Answer 18

Correlation measures the strength and direction of a linear relationship between two variables.

It can be positive, negative, or zero.

Question 19

What is the actual significance level?

Answer 19

The probability of making a Type I error in a hypothesis test.

It is also known as alpha (α).

Question 20

What is a critical region in hypothesis testing?

Answer 20

The region of a probability distribution which, if the test statistic falls within it, would cause the NULL HYPOTHESIS to be REJECTED.

The CRITICAL VALUE is the first value to fall inside the CRITICAL REGION.

Question 21

Define acceptance region in hypothesis testing.

Answer 21

The region of a probability distribution which, if the test statistic falls within it, would cause the NULL HYPOTHESIS to be ACCEPTED.

This region is complementary to the critical region.

Question 22

What is the actual significance level of a hypothesis test?

Answer 22

The probability of the test statistic falling in the critical region, assuming the null hypothesis is correct.

This level indicates the likelihood of making a Type I error.

Question 23

In hypothesis testing, what does the alternative hypothesis represent?

Answer 23

The hypothesis that indicates a change or relationship exists.

It is often denoted as H1 or Ha.

Question 24

True or false: The null hypothesis assumes that there is no change or relationship.

Answer 24

TRUE

The null hypothesis is typically denoted as H0.

Question 25

In the binomial distribution, what does the **critical region** depend on?

Answer 25

The type of alternative hypothesis being tested. ## Footnote This affects how the critical values are determined.

Question 26

What is the **critical region** for a test at the 5% significance level?

Answer 26

The region where the test statistic would lead to rejection of the null hypothesis. ## Footnote It is typically defined by the critical values determined from the distribution.

Question 27

What is the **binomial distribution** used for in hypothesis testing?

Answer 27

To model the number of successes in a fixed number of independent Bernoulli trials. ## Footnote It is particularly useful for tests involving proportions.

Question 28

What does the **sample mean distribution** represent in hypothesis testing?

Answer 28

The distribution of sample means from a population. ## Footnote It is used to make inferences about the population mean.

Question 29

What is the **standard error** in the context of hypothesis testing?

Answer 29

The standard deviation of the sample mean distribution. ## Footnote It quantifies the variability of sample means around the population mean.

Question 30

What is the purpose of finding the **critical region** in a normal distribution hypothesis test?

Answer 30

To determine the region where, if the sample mean falls, the null hypothesis will be rejected. ## Footnote This is essential for making statistical inferences.

Question 31

In hypothesis testing, what does the **test statistic** represent?

Answer 31

A statistic obtained from a sample used to evaluate the null hypothesis. ## Footnote It is compared against the critical region to make a decision.

Question 32

What is the **significance level** in hypothesis testing?

Answer 32

The probability of making a Type I error. ## Footnote It is the threshold for determining whether to reject the null hypothesis.

Question 33

What is the **mean** in the context of a normally distributed random variable?

Answer 33

The average value of the distribution. ## Footnote It is a key parameter in defining the normal distribution.

Question 34

What does a **two-tailed test** imply in hypothesis testing?

Answer 34

Testing for the possibility of an effect in both directions. ## Footnote This means the critical region is split between both tails of the distribution.

Question 35

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

Answer 35

The probability of observing a test statistic as extreme as, or more extreme than, the one obtained, under the null hypothesis. ## Footnote It is used to determine the significance of the results.

Question 36

What is the **null hypothesis** in a criminal trial context?

Answer 36

There is no change or relationship ## Footnote The suspect is considered innocent until proven guilty.

Question 37

What does the **alternative hypothesis** indicate?

Answer 37

There is a change or relationship ## Footnote Significant evidence to suggest the suspect is guilty.

Question 38

Define the **significance level** in hypothesis testing.

Answer 38

The percentage chance of incorrectly rejecting the null hypothesis ## Footnote The largest chance allowed for being wrong if a guilty verdict is given.

Question 39

What is the **test statistic**?

Answer 39

A statistic obtained from a sample in reference to the claim ## Footnote Represents the evidence in the trial.

Question 40

What is a **Type I error**?

Answer 40

Rejecting H0 when it is actually true ## Footnote This means concluding the suspect is guilty when they are innocent.

Question 41

What is a **Type II error**?

Answer 41

Accepting H0 when it is actually false ## Footnote This means concluding the suspect is innocent when they are guilty.

Question 42

In hypothesis testing, how is the probability of errors determined?

Answer 42

Using **conditional probability** ## Footnote This can only be calculated given the true population parameter.

Question 43

What assumptions are made about the sample used for any hypothesis test?

Answer 43

* Random sample * Representative of the population * Independent participants

Question 44

When is the Binomial hypothesis test appropriate?

Answer 44

For tesing the proportion within a population

Question 45

When is the PMCC hypothesis test appropriate?

Answer 45

For testing the association between two variables which follow a bivariate normal distribution

Question 46

When is the SRCC hypothesis test appropriate?

Answer 46

For testing the association between two variables which DO NOT follow a bivariate normal distribution

Question 47

What is the null hypothesis for every PMCC hypothesis test?

Answer 47

Question 48

Which parameter is used for a Binomial hypothesis?

Answer 48

Question 49

What parameter is used for a PMCC hypothesis?

Answer 49

Question 50

What parameter is used for an SRCC hypothesis?

Answer 50

Question 51

What pararmeter is used for a normal distribution hypothesis?

Answer 51

Question 52

What is the formal name of a binomial test?

Answer 52

One-sample binomial proportion test

Question 53

What is the formal name of a normal test?

Answer 53

One-sample z-test

Question 54

If the significance level is not stated, what should you do?

Answer 54

You should assume that it is 5%.

Question 55

If using the critical value/region method, which two values should be compared?

Answer 55

Test Statistics vs. Critical Value

Question 56

If using the p-value method, which two values should be compared?

Answer 56

p-value vs. significance level | 2TT-for p-value method to find the full p-value double the prob found