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Sagot :
A distribution of the means of two independent groups serves as the comparison distribution for an independent-samples t-test.
By using the one-sample t-test formula
If s is the sample standard deviation, n is the sample size, and x is the sample mean, is the population mean.
The between-groups variance measures the variability of the group means, whereas the within-groups variance measures the variability of the individual scores within the groups. This is a key distinction between variance terms for between-groups and within-groups.
By using the formula,
df = (n1 - 1) + (n2 - 1) (n2 - 1)
where the sample sizes for the two groups are n1 and n2.
The mean of the differences between the scores in the two groups can be used to compute the mean of the difference scores for the original data. The mean of the difference scores would be determined as follows, for instance, if the first group has scores of 3, 5, and 7, while the second group has scores of 4, 6, and 8.
[tex]\frac{(3 - 4) + (5 - 6) + (7 - 8)}{3}[/tex]
= [tex]\frac{(-1 + -1 + -1)}{3}[/tex]
= [tex]\frac{- 3}{3}[/tex]
= -1
The name of the statistical test, the sample sizes, the averages and standard deviations of the groups, the estimated t-value and degrees of freedom, and the p-value would all be included in a report of statistical results that follows proper APA format. The research question and hypothesis being examined should be stated clearly in the report, together with a discussion of the findings and their implications.
The standard error of the difference scores for the provided data can be calculated as
SE = [tex]((\frac{s12}{n1}) + (\frac{s22}{n2}))[/tex]
where n1 and n2 are the sample sizes, s1 and s2 are the standard deviations of the two groups, and
Calculating the t-value and comparing it to the critical value of t from the appropriate degrees of freedom in the t-distribution is the fifth step in performing a single-sample t-test. The null hypothesis can be rejected if the estimated t-value is greater than the critical value since it shows that the observed differences between the sample and the population are statistically significant.
To learn more about null hypothesis: https://brainly.com/question/25263462
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