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Chapter 14: Problem 16

After testing several thousand high school seniors, a state department of education reported a statistically significant difference between the mean GPAs for female and male students. Comments?

Short Answer

Expert verified
A reported statistically significant difference between the GPAs of female and male students implies that the chance didn't likely cause the difference. However, we cannot infer the size or practical significance of this difference from the statement, nor can we ascertain its causes without knowing more about the study's design and controlling factors.

Step by step solution

01

Understand Key Terms

Take note of the key terms in the exercise: statistically significant difference and mean GPAs for female and male students. The former refers to a result that's unlikely to have happened by chance, while the latter refers to average grades attained by male and female students.
02

Consider the Implication of the Statement

Reflect on the implications of the reported result. The state department of education found a statistically significant difference between the average GPAs of the female students and male students. This means the difference was not likely due to chance.
03

Formulate the Comment

Based on these insights, one could say: 'If the state department of education reports a statistically significant difference between the GPAs of female and male students, it means that this difference isn't likely by chance. However, this statement does not provide information on the size or the practical significance of this difference. Also, without knowing the context, further surrounding factors, and the overall study design, one cannot make conclusions about the causes of this difference.'

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Most popular questions from this chapter

Recall that in Question 14.3 , a psychologist determined the effect of instructions on the time required by subjects to solve the same puzzle. For two independent samples of ten subjects per group, mean solution times, in minutes, were longer for subjects given "difficult" instructions \((\bar{X}=15.8, s=8.64)\) than for subjects given "easy" instructions \((\bar{X}=9.0, s=5.01)\). A t ratio of 2.15 led to the rejection of the null hypothesis. (a) Given a standard deviation, \(s_{p}\), of \(7.06,\) calculate the value of the standardized effect size, \(d\). (b) Indicate how these results might be described in the literature.

Find the approximate \(p\) -value for each of the following test results: (a) one-tailed test, upper tail critical; \(d f=12 ; t=4.61\) (b) one-tailed test, lower tail critical; \(d f=19 ; t=-2.41\) (c) two-tailed test; \(d f=15 ; t=3.76\) (d) two-tailed test; \(d f=42 ; t=1.305\) (e) one-tailed test, upper tail critical; \(d f=11 ; t=-4.23\) (Be careful!) )

Indicate (Yes or No) whether each of the following statements is a desirable property of Cohen's \(d\). (a) immune to changes in sample size (b) reflects the size of the \(p\) -value (c) increases with sample size (d) reflects the size of the effect (e) independent of the particular measuring units (f) facilitates comparisons across studies (g) bypasses hypothesis test

Indicate which member of each of the following pairs of \(p\) -values describes the more rare test result: \(\left(\mathbf{a}_{1}\right) p>.05\) \(\left(\mathbf{a}_{2}\right) \quad p<.05\) \(\left(\mathbf{b}_{1}\right) p<.001\) \(\left(\mathbf{b}_{2}\right) p<.01\) \(\left(\mathbf{c}_{1}\right) p<.05\) \(\left(\mathbf{c}_{2}\right) p<.01\) \(\left(\mathbf{d}_{1}\right) p<.10\) \(\left(\mathbf{d}_{2}\right) \quad p<.20\) \(\left(\mathbf{e}_{1}\right) \quad p=.04\) \(\left(\mathbf{e}_{2}\right) \quad p=.02\)

To determine whether training in a series of workshops on creative thinking increases IQ scores, a total of 70 students are randomly divided into treatment and control groups of 35 each. After two months of training, the sample mean IQ \(\left(\bar{X}_{1}\right)\) for the treatment group equals 110 , and the sample mean IQ \(\left(\bar{X}_{2}\right)\) for the control group equals 108. The estimated standard error equals 1.80 . (a) Using \(t\), test the null hypothesis at the .01 level of significance. (b) If appropriate (because the null hypothesis has been rejected), estimate the standardized effect size, construct a 99 percent confidence interval for the true population mean difference, and interpret these estimates.
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