Use the Data Given Below to Verify That the T $$\begin{array} { c | c } \mathrm { A } & \mathrm { B } \\\hline 10 & 19 \\29 & 18 \\11 & 27 \\19 & 30 \\15 & 18 \\16 & 21\end{array}$$

question 80

Essay

Use the data given below to verify that the t test for independent samples and the ANOVA method are
equivalent. $$\begin{array} { c | c } \mathrm { A } & \mathrm { B } \\\hline 10 & 19 \\29 & 18 \\11 & 27 \\19 & 30 \\15 & 18 \\16 & 21\end{array}$$ i) Use a t test with a 0.05 significance level to test the claim that the two samples come from populations with
the same means.
ii) Use the ANOVA method with a 0.05 significance level to test the same claim.
iii) Verify that the squares of the t test statistic and the critical value are equal to the F test statistic and critical
value.

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Definitions:

Standard Deviations

Measures of the amount of variation or dispersion of a set of values, indicating how spread out the values are from the mean.

Population Variances

A measure of the dispersion of a population data set, representing the average of the squared differences from the Population Mean.

Test Statistic

A value calculated from sample data during a hypothesis test, used to determine the likelihood of a hypothesis being true.

Level of Significance

The threshold in hypothesis testing that determines whether a p-value indicates a statistically significant result, typically set at 0.05 or 5%.