One Sample Test of Hypothesis and Significance in Data Analysis
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Questions and Answers

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?

<p>When the null hypothesis is false, but it is not rejected (A)</p> Signup and view all the answers

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

<p>Increases the chance of Type I error (C)</p> Signup and view all the answers

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

<p>There is no significant difference between sample mean and population mean (A)</p> Signup and view all the answers

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

<p>Decreasing one error type increases the other error type (D)</p> Signup and view all the answers

How does a lower alpha level impact Type II error?

<p>Increases the risk of a Type II error (A)</p> Signup and view all the answers

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

<p>Alpha (α) (A)</p> Signup and view all the answers

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

<p>Higher chance of correctly rejecting a false null hypothesis (D)</p> Signup and view all the answers

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

<p>To set the threshold for rejecting the null hypothesis (B)</p> Signup and view all the answers

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

<p>If z &lt; -1.96 (C)</p> Signup and view all the answers

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

<p>$\dfrac{n(x - \mu)}{s}$ (C)</p> Signup and view all the answers

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

<p>The population variance is equal to a specific value (B)</p> Signup and view all the answers

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

<p>To understand the variability within the data (D)</p> Signup and view all the answers

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

<p>If z &gt; 1.96 (A), If z &gt; 1.96 (B)</p> Signup and view all the answers

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

<p>$t$-distribution (A)</p> Signup and view all the answers

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

<p>$0.01$ (A)</p> 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?

<p>$\chi^2$ distribution (B)</p> Signup and view all the answers

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

<p>|z| &gt; critical value (C)</p> Signup and view all the answers

What does the null hypothesis represent in hypothesis testing?

<p>The status quo assumption unless there is evidence to the contrary (A)</p> Signup and view all the answers

Which symbol is typically used to denote the null hypothesis?

<p>H0 (D)</p> Signup and view all the answers

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

<p>There is a significant difference, effect, or relationship in the population (B)</p> Signup and view all the answers

What does H1 represent in hypothesis testing?

<p>The opposite of H0 (B)</p> Signup and view all the answers

Which statement accurately describes the null hypothesis?

<p>It represents the assumption that there is no change or difference in the population (A)</p> Signup and view all the answers

What purpose does the null hypothesis serve in hypothesis testing?

<p>To act as a default assumption unless proved otherwise (A)</p> Signup and view all the answers

Which of the following best describes the alternate hypothesis?

<p>It asserts a significant difference, effect, or relationship in the population (D)</p> Signup and view all the answers

What role does statistical testing play in determining about hypotheses?

<p>To determine if sample data provides enough evidence to reject or fail to reject a hypothesis (D)</p> Signup and view all the answers

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

<p>It implies failing to reject H0 requires weak statistical evidence. (A)</p> Signup and view all the answers

What statement accurately describes the relationship between H0 and H1?

<p>H1 contradicts H0. (D)</p> Signup and view all the answers

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