Statistics and Probability Answers

Activity 2

Find the rejection region for each hypothesis test based on the information given.

1 H₂ μ = 121

Hah > 121 Η μ=986

2. Ho:μ=986 Ị Hai =27

HaiH <27

a= 0.01

a= 0.05 a= 0.05

n=34

known unknown

n=25 n=12

a known

ASSESSMENT

Perform as indicated

In numbers 1-5, find the critical valuets) and rejection remonts) for the type of z-test with level of significance a Include a graph with your answer

1 Left -tailed test, a=0.03

2 Right-tailed test = 0.05

3 Two-tailed test, a = 0.02

4 Two-tailed test, a = 0.10 5 Left-tailed test, a=0,09

In numbers 6-9, state whether each standardized test statistic z allows you to reject the null hypodesis Explain your reasoning

6. z=-1301 7 z=1203

8 2 1.280 9 2=1.286

10 A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no

more than 920 milligrams A random sample of 44 breakfast sandwiches has a mean sodium content of 925 milligrams Aanume the population standard deviation is 15 milligrams At a=0.10, do you have enough evidence to reject the restaurant's claim?

Activity 3 region

Find the critical value of each given problem. Skatch the curve and shade the wjection

1 14-90

The sample mean is 69 and simple size is 35 The population follows a normal distritsation with standard deviation 5 Usca w 0.05

2. A redaurant cashier claimed that the average amount spent by the endomers for dinner is P125.00 Over a month period, a sample of 50 customers was selected and it was found that the everage amount spent for dinner was P130.00 Using 005 level of significance can it be concluded that the average amount spent by customers is more than P125.00 Astose that the population standard deviation is 7.00

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