Statistics and Probability Answers

How large a sample should one select to be 86% confident that the sampling error is 10 or less? Assume that the population standard deviation is 250.

a. 1360
b. 890
c. 820
d. 280

If a simple random sample of 200 provides 50 'yes' responses, the 89% confidence interval for the population proportion is

a. 49.951 to 199.951.
b. .201 to .299.
c. 199.951 to 200.049.
d. 44.4 to 55.6.

Suppose a new production system will be implemented if a hypothesis test supports the conclusion that the new system increases production. Current system mean = 400

The appropriate null and alternative hypotheses in this case are?

a. Ho: µ ≥ 400 Ha: µ < 400
b. Ho: µ ≤ 400 Ha: µ > 400
c. Ho: µ = 400 Ha: µ ≠ 400
d. Ho: µ = 0 Ha: µ ≠ 0
e. Ho: µ ≠ 400 Ha: µ = 400

The new system was monitored for 40 hours and showed a mean production rate of 410 units per hour. Based on prior experience, a population standard deviation of 50 units can be used. Assume a .05 level of significance.

What is the critical value of the test statistic?

a. z = 1.96
b. t = 1.26
c. z = 1.26
d. t = 1.685
e. z = 1.64

What is the hypothesis test conclusion?

a. Do not reject Ho.
b. The test is inconclusive.
c. Reject Ho.
d. Reject Ho.
e. Do not reject Ho.

The calculated value of the test statistic is

a. z = 1.64.
b. z = 1.96.
c. t = 1.685.
d. t = 1.26.
e. z = 1.26.

Sample 1: n1 = 50, sample mean = 22, Standard deviation = 4
Sample 2: n2 = 35, sample mean = 14, Standard deviation = 5

The 90% confidence interval for the difference between the two population means is?

The 97% confidence interval for the difference between the two population means is?

The joint distribution of two variables X and Y are given below. Evaluate the following (i) Marginal distribution of X and Y (ii) E(XY) (iii) (iv) COV(X,Y),
(v) P(X + Y>1) and verify that X and Y are not independent.

Y
X 0 1
0 0.1 0.2
1 0.4 0.2
2 0.1 0

A biochemist mixed 6 chemicals together in a solution and created a new synthetic drug. Unfortunately, the biochemist does not recall the order in which the chemicals were introduced into the solution. It is decided to repeat the experiment. How many possibilities are there?

The amount of time that an electrician requires to switch on the generator in a theater when the power goes off is a random variable having an exponential distribution with a mean of 4 minutes. What is the Probability that the electrician requires less than 2 minutes on atleast 4 of the next 6 days to switch on the generator.

1. A class has 10 boys and 5 girls. Three students are selected at random one after another. Find the probability that
(i) first two are boys and third is girl (ii) first and third are of same sex and the second is of opposite sex.

(b The joint distribution of two variables X and Y are given below. Evaluate the following (i) Marginal distribution of X and Y (ii) E(XY) (iii) (iv) COV(X,Y),

(v) P(X + Y>1) and verify that X and Y are not independent.

Y X 0 1

0 0.1 0.2

1 0.4 0.2

2 0.1 0

The following data show systolic blood pressure levels (mm Hg) of a random sample of six
patients undergoing a particular drug therapy for hypertension.
182 179 154 161 170 151
Can we conclude, on the basis of these data, that the population mean is greater than 165?
Hint: Use an appropriate parametric test, at the 5% significance level.