16 One and Two Sample Hypothesis Tests

Question 1

What is the Alternative Hypothesis in hypothesis testing?

Answer 1

H1 - A statement that indicates the presence of an effect or a difference

It is the hypothesis that researchers aim to support through statistical evidence.

Question 2

Define Binomial in the context of statistics.

Answer 2

A distribution that models the number of successes in a fixed number of independent trials which all have two possible outcomes and a constant probability of success

Each trial has two possible outcomes: success or failure.

Question 3

What does the Central Limit Theorem state?

Answer 3

• for samples which are large (𝑛 ≥ 30)
• if the underlying data is not normally distributed
• then we can approximate the sample mean distribution

Question 4

What is a Critical Region in hypothesis testing?

Answer 4

The set of all values of the test statistic that would lead to the rejection of the null hypothesis

It is determined by the significance level of the test.

Question 5

What is a Critical Value?

Answer 5

The threshold value that the test statistic must exceed to reject the null hypothesis

It is derived from the significance level and the distribution of the test statistic.

Question 6

What is meant by Significance Level?

Answer 6

The probability of rejecting the null hypothesis when it is true

Commonly denoted by alpha (α), often set at 0.05.

Question 7

What is a Type I Error?

Answer 7

The error made when the null hypothesis is rejected when it is actually true

This is also known as a false positive.

Question 8

What is a Type II Error?

Answer 8

The error made when the null hypothesis is not rejected when it is actually false

This is also known as a false negative.

Question 9

What does Pooled Estimate refer to?

Answer 9

An estimate of the common variance from two or more samples

It is used when the variances of the populations are assumed to be equal.

Question 10

What is the Null Hypothesis?

Answer 10

A statement that there is no effect or no difference

It serves as the default assumption that is tested against the alternative hypothesis.

Question 11

What is a Test Statistic?

Answer 11

A standardised value that is calculated from sample data during a hypothesis test

It is used to determine whether to reject the null hypothesis.

Question 12

What is the t-Distribution?

Answer 12

A type of probability distribution that is symmetric and bell-shaped, similar to the normal distribution

It is used when the sample size is small and the population standard deviation is unknown.

Question 13

What is the Power of a test?

Answer 13

The probability that the test correctly rejects a false null hypothesis

It is the likelihood of avoiding a Type II error.

Question 14

What is an Unbiased Estimate?

Answer 14

An estimate that is expected to equal the parameter it estimates

For a sample from Y; the unbiased estimate for μ is ȳ and for σ is s

Question 15

What is the Difference in hypothesis testing?

Answer 15

The comparison of two population parameters, such as means or proportions

It is often the focus of hypothesis tests.

Question 16

What assumptions need to be made for a difference of means, t-test?

Two sample t-test

Answer 16

• Normality of data
• Independent samples
• Equal variances

Question 17

What is the pooled proportion for the unknown population proportion?

Answer 17

Calculated from the combined proportions of both samples

Used in hypothesis testing for differences in proportions - in he formula booklet

Question 18

What are the assumptions for a two sample binomial proportion test?

Answer 18

• Independent Samples
• np>10 and n(1-p)>10 for both populations
• Both populations meet the binomial conditions

Question 19

What assumption must be made about the underlying population to perform a one-sample t-test?

Answer 19

The data follows a normal distribution

Question 20

What assumptions need to be made for a difference of means, z-test?

Two sample z-test

Answer 20

• Both samples are taken from NORMALLY DISTRIBUTED POPULATIONS or the CENTRAL LIMIT THEOREM applies
• The VARIANCES (and therefore standard deviations) are KNOWN for each distribution
• The two normal distributions are INDEPENDENT

Question 21

What are the hypotheses for a one sample t-test?

Answer 21

Question 22

What are the hypotheses for a difference of two means test?

Can be for both z or t

Answer 22

Question 23

What are the hypotheses for a two sample binomial proportion test?

Answer 23