T-test Analysis and Hypothesis Testing

<p>The results are statistically significant. (D)</p> Signup and view all the answers

<p>Data points are varied and spread out from the mean. (C)</p> Signup and view all the answers

<p>Group 2 (C)</p> Signup and view all the answers

<p>22 (B)</p> Signup and view all the answers

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

<p>To determine if differences in means are likely due to chance. (C)</p> Signup and view all the answers

<p>$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$ (D)</p> Signup and view all the answers

<p>The groups must have equal sample sizes. (B)</p> Signup and view all the answers

<p>14 (A)</p> Signup and view all the answers

<p>Measuring the same group's performance before and after a training program. (C)</p> Signup and view all the answers

<p>When analyzing data from more than two groups. (D)</p> Signup and view all the answers

<p>Compare it to a theoretical value from the t-distribution. (B)</p> Signup and view all the answers

<p>The risk of incorrectly rejecting the null hypothesis (B)</p> Signup and view all the answers

<p>Performing a regression analysis (B)</p> Signup and view all the answers

<p>It assesses equality and differences simultaneously (A)</p> Signup and view all the answers

<p>The data must exhibit normality and independence (D)</p> Signup and view all the answers

<p>μ ≥ 23 (C)</p> Signup and view all the answers

<p>Excel and SPSS (B)</p> Signup and view all the answers

<p>To guarantee the accuracy and completeness of results (D)</p> Signup and view all the answers

<p>To compare the sample mean to a theoretical mean (C)</p> Signup and view all the answers

<p>The sample should be drawn from a normally distributed population (D)</p> Signup and view all the answers

<p>μ &gt; 23 (C)</p> Signup and view all the answers

<p>When measuring the same group before and after an intervention. (B)</p> Signup and view all the answers

<p>The t-distribution accounts for the sample standard deviation rather than the population standard deviation. (C)</p> Signup and view all the answers

<p>Independent two-sample t-test (A)</p> Signup and view all the answers

<p>The independent variable should be categorical and the dependent variable should be continuous. (C)</p> Signup and view all the answers

<p>As sample size decreases, the t-distribution becomes wider and flatter. (A)</p> Signup and view all the answers

<p>Both B and C (B)</p> Signup and view all the answers

<p>The number of independent pieces of information in the sample. (B)</p> Signup and view all the answers

<p>When comparing means across three or more independent groups. (D)</p> Signup and view all the answers

<p>To investigate differences within a single group at two different times. (A)</p> Signup and view all the answers

<p>Understanding the relationship between independent and dependent variables is crucial. (D)</p> Signup and view all the answers

<p>It assesses whether the mean of a single group differs from a predefined standard value. (D)</p> Signup and view all the answers

<p>To determine if a population mean is equal to a specific value. (B)</p> Signup and view all the answers

<p>Total observations minus 2. (D)</p> Signup and view all the answers

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

<p>The mean is greater than or less than a specific value. (D)</p> Signup and view all the answers

<p>It is unknown, so the sample standard deviation is utilized instead. (D)</p> Signup and view all the answers

<p>It measures differences at two different points in time within the same group. (A)</p> Signup and view all the answers

<p>A single sample measured at two different times. (A)</p> Signup and view all the answers

<p>To determine if the average height of a new group of students matches a standard value. (B)</p> Signup and view all the answers

A statistical test used to compare the means of two groups, assuming that the data is normally distributed.

The probability of obtaining the observed results, or more extreme results, if there is no real difference between the groups being compared.

A value that measures the effect size or the magnitude of the difference between two groups.

The number of independent pieces of information used to calculate a statistic. It is typically the number of observations minus the number of estimated parameters.

A statistical software tool used to determine the appropriate sample size needed for a study, based on desired statistical power, effect size, and alpha level.

A result is not statistically significant when the p-value is greater than 0.05.

The probability of detecting a true effect, or the probability of finding a statistically significant result if there is a real difference between the groups.

A value that represents the difference between the means of two groups, adjusted for the variability of the data.

A statistical test used to determine if there is a significant difference between two groups.

A statistical test used to determine if there is a significant difference between two measurements taken from the same group at different times.

A statistical test used to determine if there is a significant difference between a sample mean and a known population mean.

A hypothesis test that tests whether the population mean is greater than or less than a specific value.

A hypothesis test that tests whether the population mean is equal to a specific value.

The statement that there is no difference between the groups being compared.

The statement that there is a difference between the groups being compared.

The level of significance in a hypothesis test is the threshold for rejecting the null hypothesis.

The t-distribution models the standardized difference between a sample mean and the population mean when the population standard deviation is unknown and the data comes from a normal distribution.

It's a measure of the information used to estimate the population variance. The more degrees of freedom, the more confident we are in our estimation.

This t-test is used to compare means of two related samples, typically from the same subjects at different times.

Used when data is not normally distributed and violates assumptions of parametric tests. Examples include the Wilcoxon signed-rank test and Mann-Whitney U test.

This test compares the means of two or more groups to determine if there's a significant difference amongst them.

This test assesses whether there's an association between two categorical variables.

A statistical technique that uses hypothesis testing to draw conclusions about population parameters based on sample data.

A statistical test used to compare the means of two groups.

The proposed explanation for a phenomenon that we are trying to disprove. It assumes no difference between groups.

The alternative explanation for the phenomenon, which we are trying to prove. It claims a difference between groups.

The probability of incorrectly rejecting the null hypothesis. A common value is 0.05 (5%).

The assumption that the data follows a normal distribution and that the data points are independent of each other.

The data should be accurate and complete. Errors like typos can significantly impact the results.

A value calculated from the data which measures the difference between the groups. It's then compared to the t-distribution.

A probability distribution which helps in determining the likelihood of a result under the null hypothesis.

If the calculated test statistic falls within the rejection region (determined by the alpha value), the null hypothesis can be rejected. This suggests evidence for the alternative hypothesis.

If the calculated test statistic falls within the acceptance region, we fail to reject the null hypothesis. This does not mean it's true, but there is insufficient evidence to reject it.

A statistical test used to compare the means (averages) of two groups of data. It helps determine if the observed difference between the means is statistically significant or just due to chance.

A t-test requires the data to be continuous, meaning the variable can take on any value within a range. Examples include height, weight, or temperature.

A t-test compares the means of two groups, assuming each group is independent and the data from one doesn't influence the other.

A t-test assumes that the variability (spread) of data in each group is similar. If they differ significantly, it may affect the results of the test.

A t-test works best when the data in each group is approximately normally distributed, meaning the data is symmetrical around the mean.

A t-test is used in situations where you want to compare the means of two groups. It can inform you whether the difference between the two means is likely real or simply due to chance.

If you have more than two groups, a t-test isn't appropriate. Instead, use alternative tests like ANOVA or Tukey's HSD test, which are designed for multiple group comparisons.