12.Assume X is a continuous random variable with the following pdf:

 Find P(X>1)=?
(A)1/8
(B)1/4
(C)3/8
(D)1/2
(E)5/8

1.In hypothesis testing, (A)the smaller the Type I error, the smaller the Type II error will be (B)the smaller the Type I error, the larger the Type II error will be (C)Type II error will not be affected by Type I error (D)the sum of Type I and Type II errors must equal to 1 (E)A test with a 95% confidence level means that there is a 95% chance of getting a type I error.

2.Based on the density diagram, choose a set of hypotheses test regarding the population mean from the following (A)H₀:μ=15 v.s. Hₐ:μ<15 (B)H₀:μ=15 v.s. Hₐ:μ>15 (C)H₀:μ=0 v.s. Hₐ:μ>0 (D)H₀:μ=0 v.s. Hₐ:μ<0 (E)H₀:μ=0 v.s. Hₐ:μ>15

3.We are interested in conducting a study to determine the percentage of voters of a state would vote for the incumbent governor. What is the minimum sample size needed to estimate the population proportion with a margin of error of .05 or less at 95% confidence? (A)1068 (B)100 (C)770 (D)385 (E)58

4.The following table shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed. The calculated value for the test statistic equals (A)0 (B)2 (C)4 (D)6 (E)8

5.What is meant by the term "90% confident" when constructing a confidence interval for a mean? (A)If we took repeated samples, approximately 90% of the samples would produce the same confidence interval. (B)If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean. (C)If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean. (D)If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples. (E)We are 90% confident that 90% of the data falls within the confidence interval.

6.The test for goodness of fit. (A)is always an upper tail test. (B)is always a lower tail test. (C)is always a two-tailed test. (D)can be a lower or an upper tail test. (E)compares observed and expected means.

7.The producer of a certain bottling equipment claims that the variance of all their filled bottles is .027 or less. A sample of 30 bottles showed a standard deviation of 10 ounces. The p-value for the test is (A)less than 0.01 (B)between 0.01 and 0.025 (C)between 0.025 and 0.05 (D)between 0.05 and 0.1 (E)larger than 0.1

8.Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. =12+1.8X, n=17, SSR=225, SSE=75, σ̂b₁=0.2683  The F statistic computed from the above data is (A)3 (B)45 (C)48 (D)50 (E)60.

9.Suppose the number of car accidents per day follows a Poisson distribution with mean 3 in a metropolis. Find the probability that there are at least 2 car accidents in a 2-day period. (A)1-7e⁻⁶ (B)1-7e⁻³ (C)7e⁻⁶ (D)7e⁻³ (E)None of the above

10.I. The difference between the sample mean and the population mean is called the margin of error.  II. The difference between the upper limit of a confidence interval and the point estimate used in constructing the confidence interval is called the margin of error. III. The margin of error equals to half the width of a confidence interval. IV. The sampling error can either be positive or negative. Which above statement(s) is (are) correct? (A)I, III (B)I, II, III (C)II, III, IV (D)II, IV (E)I, II, III, IV

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