Statistics: T-Test and T-Distribution
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Questions and Answers

What is the primary goal of an independent-samples t-test?

  • To compare the means of more than two groups
  • To compare the means of two related groups
  • To determine if there is a statistically significant difference between two independent groups (correct)
  • To assess the difference in means of the same group at two different time points

Which type of t-test is used to compare the means of two related groups?

  • Two-Sample T-Test
  • One-Sample T-Test
  • Paired-Samples T-Test (correct)
  • Independent-Samples T-Test

What is an example of when to use an independent-samples t-test?

  • Assessing the difference in cholesterol levels before and after a dietary intervention
  • Determining if the mean BMI of a sample of individuals differs from the population mean BMI
  • Comparing the means of the same group at two different time points
  • Comparing the mean blood pressure levels between patients receiving a new drug and those receiving a placebo (correct)

What is the purpose of a paired-samples t-test?

<p>To determine if there is a statistically significant difference between two related groups (B)</p> Signup and view all the answers

What is an example of when to use a paired-samples t-test?

<p>Assessing the difference in cholesterol levels before and after a dietary intervention (A)</p> Signup and view all the answers

What is the key difference between an independent-samples t-test and a paired-samples t-test?

<p>The relationship between the groups being compared (B)</p> Signup and view all the answers

What would you use if you have more than two groups or more than two time points?

<p>Analysis of Variance (ANOVA) (C)</p> Signup and view all the answers

What is the main goal of a t-test?

<p>To determine if there is a statistically significant difference between two groups (D)</p> Signup and view all the answers

What is an example of a research question that could be answered using an independent-samples t-test?

<p>Is there a difference in the mean blood pressure levels of patients who received a new drug and those who received a placebo? (D)</p> Signup and view all the answers

What is an example of a research question that could be answered using a paired-samples t-test?

<p>Is there a difference in the mean cholesterol levels of the same group of individuals before and after a dietary intervention? (D)</p> Signup and view all the answers

What characteristic differentiates the t-distribution from the normal distribution?

<p>It has heavier tails (D)</p> Signup and view all the answers

What does the term 'degrees of freedom' in the t-distribution refer to?

<p>The sample size minus one (A)</p> Signup and view all the answers

What is one assumption of the t-test regarding the distribution of data within each group?

<p>Data should be approximately normally distributed (C)</p> Signup and view all the answers

Which t-test would you use to compare the mean of a single sample to a known population mean?

<p>One-Sample T-Test (B)</p> Signup and view all the answers

When does the t-distribution approach the shape of the standard normal distribution?

<p>As the sample size increases (B)</p> Signup and view all the answers

What is the main purpose of using a t-test in health sciences research?

<p>To compare groups or assess the significance of observed differences (C)</p> Signup and view all the answers

Which of the following is NOT a type of t-test?

<p>Two-Sample T-Test (D)</p> Signup and view all the answers

Which assumption of the t-test refers to the equality of variances within groups?

<p>Homogeneity of variance (B)</p> Signup and view all the answers

What is the one-sample t-test used to determine?

<p>If the sample mean is significantly different from a known population mean (A)</p> Signup and view all the answers

What is the main difference between the t-distribution and the normal distribution?

<p>The t-distribution has heavier tails, making it suitable for smaller sample sizes (B)</p> Signup and view all the answers

What is the purpose of using a one-sample t-test?

<p>To compare the mean of a single sample to a known population mean (B)</p> Signup and view all the answers

What is an assumption of the t-test regarding the data within each group?

<p>The data should be approximately normally distributed (D)</p> Signup and view all the answers

What happens to the t-distribution as the sample size increases?

<p>It approaches the shape of the standard normal distribution (C)</p> Signup and view all the answers

What is the role of degrees of freedom in a t-distribution?

<p>It determines the shape of the distribution (C)</p> Signup and view all the answers

What is the main purpose of using a t-test in health sciences research?

<p>To determine if there is a statistically significant difference between groups or assess the significance of observed differences (D)</p> Signup and view all the answers

What is the definition of the t-distribution?

<p>A probability distribution that is symmetric and bell-shaped (B)</p> Signup and view all the answers

What is an assumption of the t-test regarding the observations within each group?

<p>The observations should be independent of each other (C)</p> Signup and view all the answers

What is the definition of the paired-samples t-test?

<p>A type of t-test used to compare the means of two related groups (A)</p> Signup and view all the answers

What is the primary purpose of comparing the means of two independent groups?

<p>To determine if there is a statistically significant difference between them (B)</p> Signup and view all the answers

When would you use a paired-samples t-test to compare the means of two groups?

<p>When comparing the means of the same group at two different time points (A)</p> Signup and view all the answers

What is the key feature of a paired-samples t-test?

<p>Each observation in one group is paired with a corresponding observation in the other group (D)</p> Signup and view all the answers

What is the purpose of comparing the means of two related groups?

<p>To determine if there is a statistically significant difference between them (A)</p> Signup and view all the answers

What is the primary difference between an independent-samples t-test and a paired-samples t-test?

<p>One compares the means of two independent groups, while the other compares the means of two related groups (D)</p> Signup and view all the answers

When would you not use a paired-samples t-test?

<p>When comparing the means of two independent groups (B)</p> Signup and view all the answers

What is the purpose of an independent-samples t-test?

<p>To determine if there is a statistically significant difference between the groups (B)</p> Signup and view all the answers

What is an example of a research question that could be answered using an independent-samples t-test?

<p>Is there a difference in the mean blood pressure levels between patients receiving a new drug and those receiving a placebo? (B)</p> Signup and view all the answers

What is an example of a research question that could be answered using a paired-samples t-test?

<p>Is there a difference in the mean cholesterol levels before and after a dietary intervention? (B)</p> Signup and view all the answers

When would you use a different statistical test instead of a t-test?

<p>When comparing the means of more than two groups (D)</p> Signup and view all the answers

What is the primary characteristic of the t-distribution that makes it suitable for small sample sizes?

<p>Heavier tails (B)</p> Signup and view all the answers

What is the relationship between the sample size and the degrees of freedom in a t-distribution?

<p>The sample size increases as the degrees of freedom increase (B)</p> Signup and view all the answers

Which assumption of the t-test is related to the distribution of data within each group?

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

What is the primary purpose of using a one-sample t-test in health sciences research?

<p>To determine if the sample mean is significantly different from a known population mean (C)</p> Signup and view all the answers

What happens to the shape of the t-distribution as the sample size increases?

<p>It approaches the shape of the standard normal distribution (A)</p> Signup and view all the answers

What is the primary difference between the one-sample t-test and the independent-samples t-test?

<p>The number of groups being compared (A)</p> Signup and view all the answers

Which of the following is a characteristic of the paired-samples t-test?

<p>The groups being compared are related (A)</p> Signup and view all the answers

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

<p>To determine the shape of the distribution (A)</p> Signup and view all the answers

What is the assumption of the t-test related to the equality of variances within groups?

<p>Homogeneity of variance (A)</p> Signup and view all the answers

What type of t-test should be used to determine if a new drug has a different effect on blood pressure levels compared to a placebo?

<p>Independent-samples t-test (B)</p> Signup and view all the answers

Which t-test is appropriate for evaluating the same group of participants before and after a dietary intervention?

<p>Paired-samples t-test (D)</p> Signup and view all the answers

What is the primary distinction between an independent-samples t-test and a paired-samples t-test?

<p>The relationship between groups (C)</p> Signup and view all the answers

A researcher is testing whether a sample's mean BMI differs significantly from the population mean BMI. Which test should they use?

<p>One-sample t-test (C)</p> Signup and view all the answers

In which scenario would an independent-samples t-test not be appropriate?

<p>Assessing blood pressure levels before and after a treatment in the same individuals (D)</p> Signup and view all the answers

Which test would you use to compare the effect of a treatment administered to two independent groups?

<p>Independent-samples t-test (C)</p> Signup and view all the answers

If each observation in one group is matched with a corresponding observation in another group, which t-test is used?

<p>Paired-samples t-test (D)</p> Signup and view all the answers

What is the correct test to determine if there is a statistically significant difference in mean cholesterol levels before and after a treatment within the same group?

<p>Paired-samples t-test (A)</p> Signup and view all the answers

Which of the following scenarios best illustrates the use of an independent-samples t-test?

<p>Comparing mean test scores between two different schools (B)</p> Signup and view all the answers

In what scenario would a paired-samples t-test be the most suitable analysis?

<p>Comparing pre-treatment and post-treatment responses in the same group of patients (B)</p> Signup and view all the answers

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