Questions: Question 7 2 pts A sample of n=25 scores produces a t statistic of t=2.062. If the researcher is using a two-tailed test, then which of the following is the correct statistical decision? It is impossible to make a decision about H0 without more information. The researcher can reject the null hypothesis with either α=.05 or α=.01. The researcher can reject the null hypothesis with α=.05 but not with α=.01. The researcher must fail to reject the null hypothesis with either α=.05 or α=.01. Question 8 2 pts A sample is selected from a population with μ=46 and a treatment is administered to the sample. After treatment, the sample mean is M=48 with a sample variance of s^2=16. Based on this information, the size of the treatment effect, as measured by Cohen's d , is . d=0.125 d=0.001 d=0.25 d=0.50

Question 7
2 pts

A sample of n=25 scores produces a t statistic of t=2.062. If the researcher is using a two-tailed test, then which of the following is the correct statistical decision?
It is impossible to make a decision about H0 without more information.
The researcher can reject the null hypothesis with either α=.05 or α=.01.
The researcher can reject the null hypothesis with α=.05 but not with α=.01.
The researcher must fail to reject the null hypothesis with either α=.05 or α=.01.

Question 8
2 pts

A sample is selected from a population with μ=46 and a treatment is administered to the sample. After treatment, the sample mean is M=48 with a sample variance of s^2=16. Based on this information, the size of the treatment effect, as measured by Cohen's d , is .
d=0.125
d=0.001
d=0.25
d=0.50

Transcript text: Question 7 2 pts A sample of $\mathrm{n}=25$ scores produces a t statistic of $\mathrm{t}=2.062$. If the researcher is using a two-tailed test, then which of the following is the correct statistical decision? It is impossible to make a decision about $\mathrm{H}_{0}$ without more information. The researcher can reject the null hypothesis with either $\alpha=.05$ or $\alpha=.01$. The researcher can reject the null hypothesis with $\alpha=.05$ but not with $\alpha=.01$. The researcher must fail to reject the null hypothesis with either $\alpha=.05$ or $\alpha=.01$. Question 8 2 pts A sample is selected from a population with $\mu=46$ and a treatment is administered to the sample. After treatment, the sample mean is $M=48$ with a sample variance of $\mathrm{s}^{2}=16$. Based on this information, the size of the treatment effect, as measured by Cohen's d , is $\qquad$ . $\mathrm{d}=0.125$ $\mathrm{d}=0.001$ $d=0.25$ $\mathrm{d}=0.50$

Solution

Solution Steps

Solution Approach

For Question 7, we need to determine the critical t-values for a two-tailed test with a sample size of n=25, which gives us 24 degrees of freedom. We will compare the given t statistic (t=2.062) with the critical t-values for significance levels α=0.05 and α=0.01. This will help us decide whether to reject the null hypothesis.

For Question 8, Cohen's d is calculated as the difference between the sample mean and the population mean, divided by the standard deviation of the sample. We will use the given sample mean, population mean, and sample variance to compute Cohen's d.

Step 1: Determine Critical t-Values

For a two-tailed test with $ n = 25 $, the degrees of freedom is $ df = n - 1 = 24 $. The critical t-values for significance levels $ \alpha = 0.05 $ and $ \alpha = 0.01 $ are calculated as follows:

$ t_{0.05} \approx 2.0639 $
$ t_{0.01} \approx 2.7969 $

Step 2: Compare t-Statistic with Critical Values

The given t-statistic is $ t = 2.062 $. We compare this with the critical values:

For $ \alpha = 0.05 $: $ |t| = 2.062 < 2.0639 $ (do not reject $ H_0 $)
For $ \alpha = 0.01 $: $ |t| = 2.062 < 2.7969 $ (do not reject $ H_0 $)

Step 3: Calculate Cohen's d

Cohen's d is calculated using the formula: \[ d = \frac{M - \mu}{s} \] where:

$ M = 48 $
$ \mu = 46 $
$ s = \sqrt{s^2} = \sqrt{16} = 4 $

Substituting the values: \[ d = \frac{48 - 46}{4} = \frac{2}{4} = 0.5 \]

Final Answer

For Question 7, the researcher must fail to reject the null hypothesis with either $ \alpha = 0.05 $ or $ \alpha = 0.01 $. For Question 8, the size of the treatment effect, as measured by Cohen's d, is $ 0.5 $.

Thus, the answers are: