One-way Analysis of VarianceQuiz 2 Name: ANSWER KEYStat 217A pair of sociologists are interested in the effects of child abuse on the child’s verbal IQ . Three groups of children take part in a study: “abuse”, “neglect”, or “control.” Being in the “abuse” group is confirmed by an investigator; being in the “neglect” group is based on legal findings with regard to lack of adequate care; and the “control” group is selected from out-patients at a clinic. The MINITAB output is:One-way Analysis of VarianceAnalysis of Variance for IQ Source DF SS MS F PGroup 2 1090.9 545.5 16.7 0.000Error 61 1993.2 32.7Total 63 3084.1 Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev ----------+---------+---------+------Abuse 32 79.091 6.767 (---*---) Neglect 16 78.087 4.280 (-----*-----) Control 16 88.244 4.463 (----*-----) ----------+---------+---------+------ 80.0 85.0 90.0This quiz is worth 10 points. Each question is worth 1 point.1) Give an estimate of 3 244.883x is our best guess 2) Interpret the value you give in #1 in terms of this problem! The estimated mean average verbal IQ score for non-abused, non-neglected children in the control group is 88.2443) Check the assumption that the population standard deviations are the same (SHOW YOUR WORK!). Using the rule of thumb from our textbook, since none of the sample standard deviations s1 = 6.767, s2 = 4.28 and s3 = 6.463 are more than twice the others, then we may assume that the population standard deviations are equal, 321.4) Give an estimate of . is estimated by 72.568.32 MSE-10 0 10-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.5Normal ScoreResidualNormal Probability Plot of the Residuals(response is IQ)5) Check the assumption that the residuals are normal. Explain what you’re checking.Since the residuals in the normal probability plot follow a straight line, then we will assume that the residuals are normally distributed, ~ N(0,).6. State hypotheses to be tested using valid statistical notation. H0: 1=2=3Ha: at least one of the i ‘s is different than the others7. Circle One: Which of the following is evidence against Ho (and for Ha) in this test?A. When the variability among the group means is large compared to the variability within the groups.8. Do you reject H0 ? Why or why not?Reject H0 since p-value = 0.000 is tiny.9. Give a conclusion in terms of the problem. There is a significant difference between children’s mean verbal IQ scoresdepending on the level of abuse.10.Is there a group that has a significantly different mean IQ than the others? Even though a Tukey’s follow-up test has not been performed, which mean(s) appear to be larger or lower than the others?It appears that the control group with no abuse has the highest mean
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