#1 MULTIPLE CHOICE: Circle one of the following which most accurately completes the statement:

A. If a binomial distribution has p = 0.003 n = 1000, then the probabilities should be approximated by using the:

a. binomial distribution b. normal distribution

c. poisson distribution d. not enough information

B. A die is rolled 10 times. The probability of obtaining 5 threes should be determined using the formula for the:

a. hypergeometric distribution b. poisson distribution

C. A service station receives an average of 2 customers per hour. The probability that there will be no arrival within the next hour is:

a. 0 b. 0.1353

c. 0.25 d. 0.50

D. Which of the following is always true for a normal distribution?:

a. P(X ³ 8) = P(X > 7) b. P(2 < X £ 8) = P(2 £ X < 8)

c. P(X £ 5) ¹ P(X < 5) d. P(|X| £ 0.5) > P(-0.5 £ X < 0.5)

E. The standard error of the mean of a sample of size 64 from a very large population will equal ______________ times the standard error of the sample mean of size 16.

F. Our sample size criterion for using normal distribution for sample mean, if the population is not normal is:

#2. Find the following probabilities using the normal table:

#3 State if you agree or disagree. Explain your answer.

a. If X is a normal random variable with m = 50 and s = 10, then P(X = 50) = 0.5.

b. If X ~ N(1,1), the area to the left of X = -1 is 0.5

c. If the mean of a random sample of size 400 is used to estimate the mean of an infinite population with a standard deviation of 60, the probability is 0.95 that the |-m | is less than 5.

d. If we want to reduce the standard error of the mean by 50%, the sample size need to be increased by 100%

e. When sampling with replacement, the finite population correction factor can be omitted.

f. The central limit theorem applies only in situations when the sample size constitutes a large proportion of the population.

#4 The hypotheses are H_o: m = 50 and H_a: m ¹ 50 with a sample of size 36 and S = 4. What is the largest value of , which will not lead to the rejection of the null hypothesis for a = 0.02.

#5. We would like to estimate the average time all students take to study for a final exam, and we would like to be 90% confident that the estimate is within 0.5 hour of its true value, if it is known that s = 5.

a) Find the minimum number of students that need to be sampled.

b) If the sample average was 8 hours, compute the 90% confidence interval for n = 25.

#6 MULTIPLE CHOICE: Circle one of the following which most accurately completes the statement:

A. In a test of hypothesis, a indicates

a. the area of the rejection region for the null hypothesis

b. the probability of type two error

c. whether the test is one tailed or two tailed

d. the probability of accepting the null hypothesis

B. When a null hypothesis cannot be rejected, we conclude that

a. the null hypothesis is true b. the null hypothesis may be true

C. In a hypothesis test that a population mean is at least 50, it is a type I error that the mean is

a. at leat 50 when it is not b. at least 50 when it is

c. less than 50 when it is not d. less than 50 when it is

D. If a = 0.05 in a two tailed large sample test of hypothesis for a population mean, then:

a. 1.96 is a critical value b. 1.96 is a p-value

c. 1.645 is a p-value d. 1.645 is a critical value

#7 State if you agree or disagree. Explain your answer.

a. If we increase the confidence level, then we decrease the width of the confidence interval.

b. Increasing the sample size increases the probability of making a type II error.

c. Suppose we obtain a sample mean of 80 from a sample of size 100 from an infinite population with s = 50. Then the probability is 0.80 that the maximum error in estimating the population mean is at most 10.

d. If we want to change a standard error from 12 to 4 by changing the sample size, we need to multiply the original sample size by 6.

e. The expected value of the variance of the sampling distribution equals population variance..

f. The paired t-test for equality of two means will be appropriate if we select two random samples of size n from two different populations.

g. A type II error is committed whenever we reject the null hypothesis.