1.The variable z has a standard normal distribution. What is the probability z will be in the range -1 to + 2 ? (Hint:use function pnorm) (Give your answer corrected to four decimal points as 0.xxxx)

2.The probability of a defective unit in a manufacturing process has a binomial distribution with p = 0.03What is the probability of2 or more occurences in a sample of 15 units? (Hint: Probability of 2 or more is1 minus probability of 1 or less.)

3.In a certain country, the Intelligent Quotient of the citizens has a mean of 100 and a standard deviation of 16. What is the probability that a person will have an IQgreater than 130? (Give your answer corrected to four decimal points as 0.xxxx)(Hint: What is the z value corresponding to 130?)

4.The number of customers arriving per five minute period at a certain shop has a Poission distribution with a mean lambda equal to 2. What is the probability that there will be no customers arriving in the next five minute period? (Give your answercorrected to four decimal points as 0.xxxx) (HINT: No customers means 0 customers.)

5.The sample average in one sub-sample is x_a = 25.5 and the sample standard deviation is s_a = 17.3. The sample average in the second sub-sample is x_b = 40.3 and the sample standard deviation is s_b = 19.6. The size of the first sub-sample is n_a = 12 and the size of the second sub-sample is n_b = 16. We are interested in testing the null hypothesis that the ratio of variances Var(X_a)/Var(X_b) is equal to one against the two-sided alternative. The null is:

Select one:

a. Not rejected with a significance level of 5%.

b. Rejected with a significance level of 5%, but not with a significance level of 1%.

c. Rejected with a significance level of 1%, but not with a significance level of 0.1%.

d. Rejected with a significance level of 0.1%

6.Consider data regarding a response y and an explanatory variable x, both numeric:

12.80.722.61.336.8-1.143.00.254.71.165.0-0.175.00.982.91.097.0-0.2103.70.8

Data

x y

1. 2.8 0.7
2. 2.6 1.3
3. 6.8 -1.1
4. 3.0 0.2
5. 4.7 1.1
6. 5.0 0.9
7. 5.0 -0.1
8. 2.9 1.0
9. 7.0 -0.2
10. 3.7 0.8

The null hypothesis that the expected value of the response is constant for all values of the explanatory variable is:

Select one:

a. Not rejected with a significance level of 5%.

b. Rejected with a significance level of 5%, but not with a significance level of 1%.

c. Rejected with a significance level of 1%, but not with a significance level of 0.1%.

d. Rejected with a significance level of 0.1%

7.An experiment that deals with the mental relation between weapon and aggression was considered in the Assignment for Unit 8. One of the variables in the experiment was "aw", the time of reaction for an aggressive target word following a weapon prime. It turns out that the average value of this variable among the 15 females that participated in the experiment is 40.33151 and the average among the 17 males is 41.43632. The sample standard deviation for female is 3.840025 and for males it is 6.371546.

The confidence interval, with confidence level of 90%, for the variance of variable "aw" among males is: (Assume a Normal distribution for the variable. Choose the interval closest to the answer)

Select one:

a. [24.70, 81.58]

b. [4.33, 10.95]

c. [38.73836, 44.13428]

d. [3.88, 12.80]

8.A coffee shop owner offers two brands of coffee, Brand "A" and Brand "B". The proportion of clients that prefer Brand "A" is 60%.

Recently, the price of Brand "A" went up. The proportion of clients that buy brand "A" among the first 15 customers that enter the shop after the change in price is an estimator of the current proportion of clients that prefer Brand "A".

Assume that the change in price has no effect on the preference of the clients. Then the mean squared error (MSE) of the estimator is equal to: (Give an answer of the form x.xxx, i.e. with 3 significance digits)

(HINT: Carefully read the definition of MSE in Chapter 10 of the text book.)