One Sample Test of Hypothesis and Significance in Data Analysis

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What is the purpose of hypothesis testing in statistics?

To make decisions about the population parameters based on sample data (correct)

To determine the null hypothesis

To collect population data

To make assumptions about the sample data

Which statement best describes the null hypothesis?

It represents what the researcher is trying to find evidence for.

It serves as the default or status quo assumption. (correct)

It assumes a relationship between variables.

It asserts a significant difference in the population.

What does the alternative hypothesis represent?

A default assumption

A status quo assumption

Opposite of the null hypothesis (correct)

No effect or difference in the population

In hypothesis testing, what does H0 usually state?

There is no change or difference in the population. Signup and view all the answers

When conducting hypothesis testing, what does H1 represent?

The opposite of the null hypothesis Signup and view all the answers

Which type of hypothesis asserts that there is no significant difference between groups being compared?

Null hypothesis Signup and view all the answers

What does H0 assume about population parameters before any evidence is collected?

It assumes there is no significant difference. Signup and view all the answers

Which hypothesis asserts that there is a significant difference, effect, or relationship in the population?

Alternative hypothesis Signup and view all the answers

True or False: The null hypothesis always states a positive effect or change in the population.

False Signup and view all the answers

What happens to the null hypothesis if there is enough evidence to reject it?

It is rejected in favor of the alternative hypothesis Signup and view all the answers

What is the purpose of the significance level in hypothesis testing?

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

In a two-tailed test, how are the z-values that cut off the tails of the standard normal distribution determined?

By finding z-values that cut off α/2 in each tail Signup and view all the answers

What is used instead of the population standard deviation in hypothesis testing when it is unknown?

Sample standard deviation Signup and view all the answers

How are the degrees of freedom calculated in a hypothesis test for a population mean?

By subtracting 1 from the sample size Signup and view all the answers

When does one reject the null hypothesis in a right-tailed test using the t-statistic?

If the calculated t-score is greater than the critical value Signup and view all the answers

What distribution is used for testing hypotheses about a population variance?

$ ilde{ ext{X}}$-distribution Signup and view all the answers

What step involves looking up critical t-values from a table in hypothesis testing for a population variance?

Determine the critical value Signup and view all the answers

In a left-tailed test for a population variance, when is the null hypothesis rejected?

If chi-square > critical value Signup and view all the answers

What step follows calculating the test statistic when using the t-distribution in hypothesis testing for a population mean?

Determine the degrees of freedom Signup and view all the answers

When determining whether to reject the null hypothesis in a two-tailed test with chi-square distribution, what condition indicates rejection?

When chi-square > critical value Signup and view all the answers

What is the purpose of hypothesis testing?

To determine if there is enough evidence to reject the null hypothesis Signup and view all the answers

Which of the following is true about Type I error?

It is the incorrect rejection of a true null hypothesis Signup and view all the answers

What does Type II error involve?

Accepting the null hypothesis when it is false Signup and view all the answers

What is a common consequence of decreasing the probability of Type I error?

Increased chance of Type II error Signup and view all the answers

What does a lower beta level signify in hypothesis testing?

Increased risk of Type II error Signup and view all the answers

When conducting a two-tailed test for population mean using z-statistic, what does rejecting the null hypothesis indicate?

Accepting that there is a significant difference between sample mean and population mean Signup and view all the answers

'Balancing Type I and Type II Errors' refers to what in hypothesis testing?

The trade-off and relationship between minimizing different types of errors Signup and view all the answers

'Power of a test' in hypothesis testing refers to what?

Ability to correctly reject a false null hypothesis Signup and view all the answers

'Type I Error' is also known as what in statistical hypothesis testing?

'False Positive' Signup and view all the answers

'Type II Error' is associated with which scenario in statistical hypothesis testing?

'Failing to reject a false null hypothesis' Signup and view all the answers