Statistics and Probability Answers

Consider a population consist of 9, 5, 6, 12, and 15. Suppose that sample size of 2were drawn from this population (without replacement), describe the sampling distribution of the sample means

The average lot size of the houses in a small village is 55 square meters with a standard deviation of 10 square meters. Find the mean of the sampling distribution of the sample mean with a sample size of 50 houses if lot sizes are normally distributed.

df= 25 Percentile= 97.5th t(a,df) =

The Head of the Mathematics Department announced that the mean score of Grade 11

students in the first validating test in Mathematics was 65 and the standard deviation was 12.

One student who believed that the mean score was less than this, interviewed 50 randomly

selected students and obtained a mean score of 60. At 0.01 level of significance, test the

student's belief.

2. A simple random sample of 15 people from a certain population has a

mean age of 35 with a standard deviation of 20. Can we conclude that

the mean age of the population is younger than 35? Let alpha = .05.

Read and analyze the following situations and supply the values of the following variables (if

there is any). On the third column, write known on the space provided if the situation gives

or can compute the value of the variance, otherwise write unknown. Identify also the formula

to be used to estimate the standard error of the mean by writing the symbols of, when the

population variance is known and sawhen the population variance is unknown,

Situation :

Given the population mean of 12, and a sample standard deviation of 3 in a sample size of 125

Given :

Answer :

Standard error formula :

If 50 of them are taken as samples, what is the probability that their mean height is less than 150cm?

What is the probability of getting a perfect square from the numbers 1 to 100?

A.

1/4

B.

1/10

C.

1/25

D.

1/5

E.

None of the above

The probability that two events, A and B, will both occur is represented by the following multiplication rule:

A.

P(A ∩ B) = P(A│B) × P(B)

B.

P (A ∩ B) = P(A) × P(B)

C.

P(A ∩ B) = P(B│A) × P(B)

D.

Both B and C.

E.

None of the above

Suppose a population consists of the ages of 5 students, as follows: 16, 17, 18, 19 and 20. Construct a sampling distribution of the sample mean using random variable of size n=2. Prepare a probability distribution of the sample means.