Statistics and Probability Answers

A population consists of five numbers 1, 2, 3, 4, 5 and 6. Suppose samples of size 2 are drawn from this population.

(a) Find the mean and variance of the population

(b) Describe the sampling distribution of the sample means.

(c) Find the mean and variance of the sampling distribution of the sample means.

Frequent checks on the spending patterns of tourists returning from countries in Asia were made and the average amount spent by all tourists was found to be R1010 per day. To determine whether there has been a change in the average amount spent, a sample of 70 travelers was selected and the mean was determined as R1090 per day with a standard deviation of R300. A researcher wants to test for evidence of a change in the expenditure amount changed, using 0.05 level of significance.

i. What is the appropriate distribution to use? Motivate your answer. [3]

ii. State your hypotheses. [2]

iii. Is there a claim? What is the claim and in which part of the hypothesis does the claim resides? [3]

iv. Use a distribution curve to determine the rejection and non-rejection region using critical values for the appropriate distribution. [5]

v. Calculate the test statistic of the distribution. [2]

vi. Compare your test statistic to the critical value. [2]

vii. State both your statistical and a management conclusion. [3]

Frequent checks on the spending patterns of tourists returning from countries in Asia were made and the average amount spent by all tourists was found to be R1010 per day. To determine whether there has been a change in the average amount spent, a sample of 70 travelers was selected and the mean was determined as R1090 per day with a standard deviation of R300. A researcher wants to test for evidence of a change in the expenditure amount changed, using 0.05 level of significance. What is the appropriate distribution to use? Motivate your answer

3. A certain report claims that less than 40% of BTS fans based on Southeast Asia come from

the Philippines.

H 0 : ___________________________________________________________

H a : ___________________________________________________________

Find each of the following percentile points

under the normal curve.

1. P76

2. P85

3. P39

4. P51

5. P88

A nationwide survey of college seniors by the

University of Michigan revealed that almost 70% disapprove of daily pot smoking, according to a report in

Parade. If 12 seniors are selected at random and asked

their opinion, find the probability that the number who

disapprove of smoking pot daily is

(a) anywhere from 7 to 9;

(b) at most 5;

(c) not less than 8

A group of students got the following scores in a test: 6, 9, 12, 15, 18, and 21. Consider samples of size 3 that can be drawn from this population

Samples of three cards are drawn at random from a population of eight cards numbered from 1 to 8.

The leader of the Factory Worker claims that the average pay of factory workers in

Marikina City is less than 500 php. A random sample of 16 factory workers was

interviewed and resulted on the average of 350 php. Using a significance level of

0.05 and standard deviation of 92. Determine if there is sufficient evidence that the

claim is true.