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The answers and explanations for selected questions from a statistics exam held in spring 2007. The questions cover topics such as hypothesis testing, confidence intervals, and t-distributions. Students are advised to check their understanding of the assumptions required for the validity of statistical tests and interpret the results correctly.
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STAT 205 Name: _____ ANSWER KEY_ Spring 2007 Exam 2
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Part I: Answer eight of the following nine questions. If you complete more than eight, I will grade only the first eight. Five points each.
State the definition of a P-value. The probability under H 0 of observing a test statistic as extreme or more extreme (in the direction of HA) as that actually observed.
(Circle the correct answer) A hypothesis test has been conducted at the 0. significance level, resulting in a P-value of 0.06. Obviously, in this case we fail toreject H0. If an error was made, it would be a Type I / Type II / neither error.
Suppose you want to analyze a sample of size n=10 and your QQplot shows a violation of normality. In practice, a transformation is commonly attempted before using a non- parametric test.
(Circle one) True / False A t -distribution based confidence interval for the mean, ,
and a t -distribution based hypothesis test for the mean, , are different forms of the same inference.
(Circle the correct answer) Twenty institutionalized epileptic patients participated in a study of a new anticonvulsant drug Valproate. Ten of the patients (chosen at random) were started on the daily Valproate and the other ten received an identical placebo pill. During an eight week observation period, the number of major and minor seizures was counted. After this, the patients were “crossed over” to the other treatment, and seizure counts were made during a second eight week observation period. We would use the independent / dependent (paired) samples method in order to conduct a test of hypothesis.
We learned several standard error of means (SEMs) for use in making inference on the population mean. In the independent samples setting, we have been applying one type of SE for the difference between two means, but you also learned of another type of SE which can be used in the independent samples setting called SE (^) pool. Describe the special situation for which we can deploy its use. We use SE (^) pool when we have reason to believe the standard deviation for the population group one came from is the same as that for the population of group two ( 1 = 2).
Part II: Answer every part of the next two problems. Read each question carefully, and show your work for full credit.
1a) (25 points) A random sample of 32 sets of twins under the above circumstances was taken. The sample mean difference (IQ twin reared by natural parent – IQ twin not reared by natural parent) in IQ scores is -2.906, the standard deviation of the differences is 8.895. Conduct a test of hypothesis to see whether there is a significant difference (at the = 0.05 significance level) in the mean IQ scores under these two conditions.
Note: This is the dependent (paired) samples setting. Let R / NR denoted reared / not reared by natural parent, respectively.
(1) α = 0.
(2) H (^) 0: μR – μNR = 0 or μR = μNR or μd = 0 H (^) A: μR – μNR ≠ 0 or μR ≠ μNR or μd ≠ 0
STAT -> scroll over to TESTS -> scroll down to T-Test
Choose “Stats”, o:0, xത: -2.906, s (^) x: 8.895, n: 32, μ: ≠o -> Calculate -> ENTER
(3) t (^) s = -1.
(4) P = 0.
(5) P > α, so fail to reject H (^0)
(6) There is not significant evidence (at the = 0.05 significance level) to conclude that when twins are reared separately, true mean IQ score differs for twins reared by natural parents versus twins who are not reared by their natural parents.
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