Statistics and Probability Answers

The diameter of steel rods manufactured on two different extrusion machines are

being investigated. Two random samples of sizes "n_1" = 15 and "n_2" = 17 are selected,

and the sample means and sample variances are x̅1 = 8.73, "s_1^2" = 0.35, x̅2 =8.68, and "s_2^2" = 0.40, respectively. Assume that "\\sigma_1^2=\\sigma_2^2"

and that data are drawn from

a normal distribution. (a) Is there evidence to support the claim that the two

machines produce rods with different mean diameters? Use α = 0.05 in arriving at

this conclusion. (b) Find the P-value for the t-statistic you calculated in part (a).

[taken from Montgomery, p. 347]

A mathematics teacher in senior high school developed a problem-solving test to randomly selected 40 grade 11 students. These students had an average score of 85 and a standard deviation of 5. If the population had a mean score of 90 and a standard deviation of 3, use 5% level of significance to test the hypothesis.

A ball is drawn from a box containing 6 red balls, 4 white balls and 5 black balls . What is the probability that it is not red ball?

Consider a population consisting of 2, 4, 6, 8 and 10. Suppose samples of size 3 are drawn from this population.

a. Describe the sampling distribution of the sample means

b. What are the mean and variance of the sampling distribution of the sample means? c. Construct a histogram for the sampling distribution.

An insurance company found that 45% of all insurance policies are terminated before their maturity

date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a

Binomial experiment.

Required:

a) What is the probability that eight policies are terminated before maturity?

b) What is the probability that at least eight policies are terminated before maturity?

c) What is the probability that at most eight policies are not terminated before maturity?

Consider a population with values 1, 2, 3, 5, 7, 11

a. Find the population mean

b. Find the population variance

c. Find the population standard deviation.

d. Find all possible samples of size 4 which can be drawn with replacement from this

population

e. Find the mean of the sampling distribution.

f. Find the variance of the sampling distribution of means.

g. Find the standard deviation of the sampling distribution of means

Compute the value of z when ƥ = 0.46, q = 0.54, n = 50 and p₀ = 0.50.

Consider a population consisting of 2, 4, 6, 8 and 10. Suppose samples of size 3 are drawn from

this population. a. Describe the sampling distribution of the sample means b. What are the mean and variance of the sampling distribution of the sample means? c. Construct a histogram for the sampling distribution.

Consider a population consisting of 2, 4, 6, 8 and 10. Suppose samples of size 3 are drawn from this population.

a. Describe the sampling distribution of the sample means

b. What are the mean and variance of the sampling distribution of the sample means? c. Construct a histogram for the sampling distribution.

Consider a population consisting of 2, 4, 6, 8 and 10. Suppose samples of size 3 are drawn from this population.

a. Describe the sampling distribution of the sample means.

b. What are the mean and variance of the sampling distribution of the sample means?

c. Construct a histogram for the sampling distribution,