Statistics and Probability Answers

a population consisits of four numbers (3,8,10,15) consider all the possible sample of size 2 that can be drawn without replacement from the population find the following

a.find the population mean

b. find the population varince

c.find the population standard deviation

d.find the possible sample of size 2 which can be drawn without replacement from this population

e.find the mean of the sampling distribution of means

f.find the varience of the sampling distribution of means

g.find the standard deviation of the sampling distribution of means .

Perform the hypothesis of the following scenarios.

The graduate record exam is standardized test recquired to be admitted to many graduate schools in the United States. A high score in GRE makes admissions more likely. According th the educational testing service, the mean score for takers of GRE who do not have training courses is 555 with standard deviation of 139. Brain Philippine offers expensive GRE training courses, claiming their graduates score better than those who have not talen any training courses. To test the company's claim, a statisticiam randomly selected 30 graduates of BP and asked their GRE scores. They recorded a mean score of 560 in GRE. Is the company's claim true, using a 95% confidence level?

Find each of the following percentile points under the normal curve.

1. P99

2. P90

3. P68

4. P40

5. P32

Find each of the following percentile points under the normal curve. 1. P99 2. P90 3. P68 4. P40 5. P32

A researcher wanted to estimate the difference between the percentages of users of two 

tooth pastes who will never switch to another tooth paste. In a sample of 500 users of 

Toothpaste A taken by this researcher, 100 said that they will never switch to another 

toothpaste. In a sample of 400 users of Toothpaste B taken by the same researcher 68 said 

that they will never switch to another toothpaste.

(i) Let p1 and p2 be the populations of all users of Toothpastes A and B, respectively who 

will never switch to toothpaste. What is the point of p1-p2? (4 marks)

(ii) Construct a 98% confidence interval for the difference between the proportions of all 

users of the two toothpastes who will never switch (6 marks)

Solve for the mean of the sampling distribution of the sample means

Suppose a population is composed of only 3 measures: 1, 2, and 3. The possible samples of size 2 can be draw from this population. List all the possible sample size 2 when repetition is allowed or with replacement. With solution

In a fuel economy study, each of 3 race cars is tested using 5 different brands of gasoline at 7 test sites located in different regions of the country. If 2 drivers are used in the study, and test runs are made once under each distinct set of conditions, how many test runs are needed?

Using the provided information below,

x=33.2 , x2=131.67, y=30.78 , y2=116.52image.png, xy=119.8 , and n=10image.png

Find the sample correlation coefficient rimage.png (4mks)

Find the co-efficient of determination

You are deciding between two portfolios; Portfolio A which is made up of stocks and treasury bills, and Portfolio B which comprises of risky bonds and treasury bills. The table below contains information on both portfolios that you collected.

Information

Portfolio A

Portfolio B

Mean returns

0,13

0,16

Standard Deviation

0,11

0,09

Expected Returns

0,15

0,12

Threshold level

0,07

0,07

a) What is the probability that the returns of Portfolio A lie between 15 and 25 percent?

b) If the probability that the returns of Portfolio B would be greater than X is 0.2676, what is the value of X?

c) Which portfolio is the optimal portfolio considering your threshold level?

d) For the optimal portfolio found in (c), what is the probability that the portfolio will earn a return below the threshold level?