Dr. Penner thinks that she can predict a person’s success at a spatial task from

Question

Dr. Penner thinks that she can predict a person’s success at a spatial task from their Mental Ability Score (MAS). She asks 300 high-school students to complete the MAS (scores range from 10-50) and a series of spatial tasks (scores range from 0-15). She expects that with increased MAS high school students will be more successful at the spatial task.

What are the test’s assumptions?

What is the appropriate critical value?

If the research obtains a test statistic of ____ , would the researcher retain or reject H0?

Should the researcher do any follow up tests or make any graphs/charts?

Interpret the findings in APA style Expert Answer

Explanation / Answer

Here dependent variable is person's success at a spatial task and independent variable is mental ability score.

We have to test the hypothesis that,

H0 : There is no relationship between variables.

H1 : There is positive relationship between variables.

Assume alpha = level of significance = 0.05

The test statistic follows t-distribution with n-2 degrees of freedoms.

The test statistic is,

t = r*sqrt(n-2) / sqrt(1-r^2)

where n is number of data pairs.

r is sample correlation between variables.

Now we have to find critical value.

Critical value we can find in excel.

syntax :

=TINV(probability, deg_freedom)

n = 300

deg_freedom = n-2 = 300-2 = 298

Critical value = 1.646

Decision rule :

If test statistic > critical value then reject H0 at 5% level of significance otherwise accept H0 at 5% level of significance.

We can graphically find the correlation by using scatter plot.

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