One Sample Test of Hypothesis and Significance in Data Analysis

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What is the purpose of hypothesis testing?

To determine the population standard deviation

To calculate the margin of error

To determine the sample size needed for a study

To determine if there is enough evidence to accept the null hypothesis (correct)

Which of the following best describes a Type I error?

Failing to reject the null hypothesis when it is true

Incorrectly rejecting the null hypothesis when it is true (correct)

Failing to reject the alternative hypothesis

Correctly rejecting the null hypothesis when it is false

What symbol is used to represent the probability of making a Type II error?

Beta (β) (correct)

Gamma (γ)

Alpha (α)

Delta (δ)

When does a Type II error occur?

When the null hypothesis is false, but it is not rejected Signup and view all the answers

What does decreasing the significance level (?) chosen for a test impact?

Increases the chance of Type I error Signup and view all the answers

In testing hypotheses about a population mean using the z-statistic, what does H0 represent?

There is no significant difference between sample mean and population mean Signup and view all the answers

What trade-off exists between Type I and Type II errors?

Decreasing one error type increases the other error type Signup and view all the answers

How does a lower alpha level impact Type II error?

Increases the risk of a Type II error Signup and view all the answers

What symbol represents the probability of making a Type I error in hypothesis testing?

Alpha (α) Signup and view all the answers

What does a higher power of a test mean in hypothesis testing?

Higher chance of correctly rejecting a false null hypothesis Signup and view all the answers

What is the purpose of determining the critical value in hypothesis testing?

To set the threshold for rejecting the null hypothesis Signup and view all the answers

In a left-tailed test, when do we reject the null hypothesis?

If z < -1.96 Signup and view all the answers

What is the formula to calculate the test statistic (t-score) when using the t-distribution?

$\dfrac{n(x - \mu)}{s}$ Signup and view all the answers

When conducting a hypothesis test for a population variance, what does the null hypothesis state?

The population variance is equal to a specific value Signup and view all the answers

What is the purpose of determining the degrees of freedom in a t-test?

To understand the variability within the data Signup and view all the answers

For a right-tailed test, when do we reject the null hypothesis?

If z > 1.96 Signup and view all the answers

Which distribution is used when the population standard deviation is unknown?

$t$-distribution Signup and view all the answers

What is the significance level often set at in statistical hypothesis testing?

$0.01$ Signup and view all the answers

What is used to determine if there is a significant difference between the variance of a sample and a hypothesized population variance?

$\chi^2$ distribution Signup and view all the answers

In a two-tailed test, what is the condition to reject the null hypothesis?

|z| > critical value Signup and view all the answers

What does the null hypothesis represent in hypothesis testing?

The status quo assumption unless there is evidence to the contrary Signup and view all the answers

Which symbol is typically used to denote the null hypothesis?

H0 Signup and view all the answers

In a hypothesis test, what does the alternative hypothesis assert?

There is a significant difference, effect, or relationship in the population Signup and view all the answers

What does H1 represent in hypothesis testing?

The opposite of H0 Signup and view all the answers

Which statement accurately describes the null hypothesis?

It represents the assumption that there is no change or difference in the population Signup and view all the answers

What purpose does the null hypothesis serve in hypothesis testing?

To act as a default assumption unless proved otherwise Signup and view all the answers

Which of the following best describes the alternate hypothesis?

It asserts a significant difference, effect, or relationship in the population Signup and view all the answers

What role does statistical testing play in determining about hypotheses?

To determine if sample data provides enough evidence to reject or fail to reject a hypothesis Signup and view all the answers

What does the default assumption imply about rejecting or failing to reject the null hypothesis?

It implies failing to reject H0 requires weak statistical evidence. Signup and view all the answers

What statement accurately describes the relationship between H0 and H1?

H1 contradicts H0. Signup and view all the answers