Statistics and Probability Answers

Compute the z-statistic for each given claim (p), the observed proportion (p^), and the given

sample size (𝑛).

𝑝 = 0.53, 𝑝̂= 0.54, 𝑛 = 32

HYPOTHESIS TESTINGABOUT POPULATION MEAN 𝝁

USING THE CRITICAL VALUE APPROACH

The records of SCA Registrar show that the average final grade in Mathematics for STEM students is 91 with a standard deviation of 3. A group of student-researchers found out that the average final grade of 37 randomly selected STEM students in Mathematics is no longer 91. Use 0.05 level of significance to test the hypothesis and a sample mean within the range of 88 to 94 only.

A. State the hypotheses.

B. Determine the test statistic to use.

C. Determine the level of significance, critical value, and the decision rule.

D. Compute the value of the test statistic.

E. Make a decision.

F. Draw a conclusion.

Compute the z-statistic for each given claim (p), the observed proportion (p^), and the given

sample size (𝑛).

𝑝 = 0.66, p^= 0.61, 𝑛 = 40

Compute the z-statistic for each given claim (p), the observed proportion (^p), and the given

sample size (𝑛).

𝑝 = 0.2, ^p= 0.18, 𝑛 = 50

A taxi driver claims that his average monthly income is Php 2, 800.00 with a standard deviation of Php 250.00 . A sample of 25 drivers were surveyed and found that their average monthly income is Php 3,500.00with a standard deviation of Php 350.00.Test the hypothesis at 1% level of significance.

A. Solve the problems by following the steps and procedures in hypothesis testing. (20 points)

1. A school teacher suspects the claim that the mean number of students that use library 

materials in a certain school is at most 450. To check the claim, the professor checks a 

random sample of 100 library records and obtain that the mean number of students 

using library materials is 458 with a standard deviation of 9. What would the teacher's 

conclusion use 0.05 level of significance? (10 points)

2. prospective MBA student was made to estimate the difference in the salaries of 

professors in private and state universities. An independent study of simple random 

samples of the most recent MBA graduates of both universities revealed the following 

statistics: Conduct a test using 0.01 level of significance. (10 points)

Salary x¯ s n

Private 52,285/mo. 2,400 49

State 50,188/mo. 2,100 49

The head of the mathematics department announced that the mean score of Grade 11 students in the second periodic test in statistics was 89, And a standard deviation was 12. One student believed that the main score was less than this, So the student randomly selected 34 students and computer do you mean score, And obtained I mean score of 85. At 0.01 level of significance, Construct the critical regions.

Find the areas under the normal curve in each of the following cases: (2pts. each)

1. Between z = 0 and z = 1.63 2. Between z = 0 and tau = 0.98

3. To the right of z= 0.29

4. To the left of

5. Between z=-1.56 and z=-1.83

z = - 1.39

The head of the mathematics department announced that the mean score of grade 11 students in the second periodic test in statistics was 89, and the standard deviation was 12. One student believed that the mean score was less than this, so thre student randomly selected 34 students and computed their mean score, and obtained a mean score of 85. At 0.01 level of significance, construct the critical regions.