Question

A researcher is interested in testing whether there is a difference in mean IQ level among people with varying levels of education (ED). For the ED variable, 1  =  no high school degree, 2  =  high school graduate, 3  =  college graduate. The researcher produces the following Minitab output. Use the Bonferonni method at the 3% significance level to test the hypothesis H₀ :  μ₁  =  μ₃  vs  H₁ :  μ₁  ≠  μ₃.

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Descriptive Statistics: IQ

ED	N	Mean	SE Mean	StDev	Minimum	Q1	Median
1	6	93.91	1.65	4.04	46.96	73.72	100.48
2	10	133.18	2.24	7.07	79.91	107.88	135.84
3	18	162.05	2.02	8.55	113.44	141.79	170.15

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Find the value of the test statistic.

(b)	[1 mark] Find the critical value.

Answer 1

Answer:

Test statistic = 19.1067

Critical value = 2.3202

Explanation:

Multiple comparison test: Bonferroni's method

Test statistic

The t statistic is obtained using the following formula,

where,

From the descriptive statistics result summary,

hence,

Critical value

The t critical value is obtained from the t critical value table for the degree of freedom = n1+n3-2= 22, significicance level = 0.03 and for two tailed test.

Conclusion:

Since the t statistic is greater than the t critical value, the null hypothesis is rejected at a 3% significance level.