Statistics and Probability Answers

Consider all samples of size 4 from this population: 3, 6, 10, 13, 15, 20

a. Make a sampling distribution of the sample means

b. Compute the mean of the sample means

c. Compute the variance and standard deviation of the sample means

2. 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 student conducted a regression analysis between the math grades of his classmates

and the number of times they were absent in the subject. He found that the regression

line y = 97.732 – 2.61x will predict grade (y) if the number of absences (x) is known.

a) What is the predicted grade of a student who has no absences?

b) What is the predicted grade of a student who has ten absences?

c) Sketch the graph of the line predictor.

Suppose that the bank customers arrive randomly and independently on an average of 3.2

customers every 4 minutes. What is the probability that:

a. Exactly two customers arrive in every 4 minutes?

At a certain college, it is estimated that approximately 19% of the students ride bicycles to school. Would you consider this to be valid estimate if, in a random sample of 85 college students, 20 are found to ride bicycles to class

A random sample of 20 drinks from a soft-drink machine has an average content of 21.9 deciliters, with a standard deviation of 1.42 deciliters. At 0.05 level of significance, test the hypothesis that μ = 22. 2 against the alternative hypothesis μ < 22.2. Assume that the distribution is normal.

A researcher claims that 13% of all motorcycle helmets have manufacturing flaws that could potentially cause injury to the wearer. A sample of 150 of these helmets revealed that 18 contained such defects.

A random sample of 20 drinks from a soft-drink machine has an average content of 21.9 deciliters, with a standard deviation of 1.42 deciliters. At 0.05 level of significance, test the hypothesis that μ = 22. 2 against the alternative hypothesis μ < 22.2. Assume that the distribution is normal.

Your given ∑ 𝑥 = 44 , ∑ 𝑥2 = 174, ∑ 𝑥𝑦 = 1324, in addition you also given the values of y

as:

Y 26 28 24 18 35 24 36 25 31 37 30 32

3a. calculate the Pearson correlation coefficient [7]

3b. estimate the y value associated with x=4 [8].

3c. You are given the mean of 20.3 for a random sample of 90 observations from a normal distribution population with a standard deviation of 3.9. Construct a 95% confidence level and interpret your answer. [3]