# Statistics Questions

Jul 20th, 2016
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True or False. Justify for full credit. (a) If P(A) = 0.4, P(B) = 0.5, and A and B are independent, then P(A AND B) = 0.9. (b) If the variance of a data set is 0, then all the observations in this data set must be zero. (c) The mean is always equal to the median for a normal distribution. (d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter. (e) In a two-tailed test, the value of the test statistic is 2. The test statistic follows a distribution with the distribution curve shown below. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.

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1. Qa.b.c.d.False: P[AunionB] = P(A) * P(B) = 0.4 * 0.5 = 0.2 != 90%.False; variance is zero and data values are non-zero.TrueTrue: A normal distribution with a mean u and variance sigma-squared has a confidenceinterval (95%) of (x +/- 1.96 sigma/sqrt(n)). For a 90% confidence interval: (x +/- 1.64sigma/sqrt(n)). The interval is below the confidence limit.e. True. The shaded area is the p-value (probability), and p<0.05. Therefore, we mustreject H0.2. Qa. Parameter: The stated percentage of Republicans is considered to be a sample of alarger population, and therefore the value is calculated as a characteristic of apopulation.b. Ordinal: The nature of the question depends upon rankings, and therefore is ordinal.c. Cluster: The total population is divided into homogenous subgroups (clusters), and arandom sample was drawn from these clusters.3. Qa. ANOVA. The test call

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