Statistics and Probability Answers

THE FOLLOWING ARE THE HEIGHT IN CENTIMETER AND HEIGHTS IN KILOGRAM OF 5 TEACHERS IN A CERTAIN SCHOOL.DETERMINE THE RELATIONSHIP BETWEEN THE HEIGHT (CM) AND WEIGHT (KG) OF THE TEACHERS

TEACHER A,B,C,D,E,F,G

HEIGHT (CM) X 163,160,168,159,170

WEIGHT (KG) Y 52,50,64,51,69

Survey tests on leadership skills and self-concept were administered to student-leaders.

Both tests use a 10-point Likert Scale, with 10 indicating the highest scores for each test.

Scores for the student-leaders on the tests follow:

Student Code A B C D E F G H I J

Self-concept 9.5 9.2 6.3 4.1 5.4 8.3 7.8 6.8 5.6 7.1

Leadership Skill 9.2 8.8 7.3 3.4 6.0 7.8 8.8 7.0 6.5 8.3

a. Compute the correlation coefficient r.

b. Interpret the results in terms of (a) strength and (b) direction of correlation.

c. Find the regression line that will predict the leadership skill if the self-

concept score is known.

d. Predict the leadership skill of a student leader whose self-concept skill is

1.5.

a. r =

=

=

=

=

=

r =

b. There is a _____________________between the self-concept skill and leadership skill of the students.

x y xy x² y²

9.5 9.2

9.2 8.8

6.3 7.3

4.1 3.4

5.4 6.0

8.3 7.8

7.8 8.8

6.8 7.0

5.6 6.5

7.1 8.3

"\\sum"= "\\sum"= "\\sum"= "\\sum"= "\\sum"=

c)

= a + bx a= ( "\\sum" y)("\\sum" x²) - ("\\sum" x)("\\sum" xy) / n("\\sum" x²) -"\\sum" x²

^{= = = a=}

b= ("\\sum" xy) - ("\\sum" x) ("\\sum" y) / n("\\sum"x² ) -("\\sum" x)²

d)= _____________

= ____________(1.5)_

= ____________

1. a) = 97.732 – 2.61x

= 97.732 – 2.61(0)

=

b) = 97.732 – 2.61x

= 97.732 – 2.61(10)

=

c) the graph

1. A certain company makes electrical cables having a mean strength of 40 kg/cm² and a standard deviation of 2 kg/cm². Assuming the strength follows a normal distribution,

a. What percentage of cables will have a strength exceeding 43 kg/cm²?

b. If strength is measured to the nearest kg/cm², what percentage of cables will have

strength exceeding 43 kg/cm²?

c. Illustrate the normal curve for a and b.

THE PRESIDENT OF A SERVICE UTILITY CLAIMS THAT 60 PERCENT OF HIS 500,000 CUSTOMERS ARE VERY SATISFIED WITH THE SERVICE THEY RECEIVE. TO TEST THIS CLAIM, THE LOCAL NEWSPAPER SURVEYED CUSTOMERS, USING SIMPLE RANDOM SAMPLING. AMONG THE SAMPLED CUSTOMERS, 64 PERCENT SAY THEY ARE VERY SATISFIED. BASED ON THESE FINDINGS, CAN WE REJECT THE PRESIDENT'S HYPOTHESIS THAT 64% OF THE CUSTOMERS ARE VERY SATISFIED? USE A 0.01 LEVEL OF SIGNIFICANCE.

II. Determine the given of the problems below and formulate the null and alternative hypothesis both in words and symbols. Write your answer in your notebook. Please follow the format in the examples.

2. A study was conducted to determine the marrying age of teachers. It was found out that the mean marrying ager of teachers is 30 years old. Fifteen teachers were surveyed randomly and found that their mean marrying age was 33 years old with a standard deviation of 5 years. Use 10% level of significance to test the hypothesis and assume that the population is normally distributed.

3. A study was conducted to determine the marrying age of teachers. It was found out that the mean marrying ager of teachers is 30 years old. Fifteen teachers were surveyed randomly and found that their mean marrying age was 33 years old with a standard deviation of 5 years. Use 10% level of significance to test the hypothesis and assume that the population is normally distributed.

In the class of Statistics, there are 75 students in total out of which 55 male, 20 female students. 10 students need to be selected for the occasion of freshers' reception.

a. Find out the mean and standard deviation of the binomial distribution.

A MNP publisher of Statistics and Probability textbooks claims that the

average price of all hardbound textbooks is Php 500. A group of students

believes that the actual mean is higher and wishes to test their belief.

Find the area to the left of critical value t = 2.500 when sample size is 24