Statistics and Probability Answers

In a certain population, it is claimed that the mean number of years of education is 13.2, while the standard deviation is 2.95 years. A random sample of 60 people is drawn from this population, and the sample mean is 13.87 years. What are the hypotheses and test statistic to be used in this case?

A population consist of three numbers (2, 4, 6). Consider all possible samples of size 2 which can be drawn without

replacement from the population. Find the following:

A population consist of three numbers (2, 4, 6). Consider all possible samples of size 2 which can be drawn without

replacement from the population. Find the following:

population mean

population variance and standard deviation

mean of each sample and the mean of the sampling distributions of means

variance of the sampling distributions of means

standard deviation of the sampling distribution of the means.

Answer what is asked in the given problem below. Show your solutions completely. Use an extra sheet of paper for your solutions. NO SOLUTIONS, NO POINTS.

The population is the weight of six pumpkins (in pounds) displayed in carnival "guess the weight" game booth. You are asked to guess the average weight of the six pumpkins by taking a random sample without replacement from the population. Suppose that the sample size of 5 pumpkins were drawn from this population (without replacement), describe the sampling distribution of the sample means.

Pumpkin

A

B

C

D

E

F

Weight in Pounds

19

14

15

9

10

17

What is the mean and variance of the sampling distribution of the sample means?

Compare these values to the mean and variance of the population.

if a population has a mean of 28.6 what is the mean of the sampling distribution of its means

Determine the given and compute the test statistic of the problem below using Central Limit Theorem, and construct the rejection region for each.

A company claimed that their N95 face mask has a mean filtration efficiency rate of 95%. A group of student researcher wanted to verify this claim. They bought and tested 40 of their N95 face masks. They found out that the average filtration efficiency rate of these face mask was 90% with a standard deviation of 4%. Test the claim at 5% level of significance and assume that the population is approximately normally distributed.

The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any one day are 0.15, 0.20,0.25,0.20, 0.20, respectively.

43.) What is the mean that a surgeon operates on patients in any one day?

 a. 5.0             b. 5.1              c. 5.2              d. 5.3              e. 5.4

44.) What is the variance of the given problem?

 a. 1.76           b.1.77             c. 1.78            d. 1.79            e. 1.80

45.) What is the standard deviation of the given problem?

 a. 1.33           b. 1.35            c. 1.37            d. 1.36            e. 1.34

State the null and alternative hypothesis for each statement.

1. The average age of bus drivers in metro manila is 39 years old.

Ho : _______________

Ha: _______________

a researcher reports that the average salary of a teacher php 27000 a sample of 32 teachers has a mean of php 29500 at a=0.01 test the claim that the co teachers earn more than php 27000 a months the standard deviation of the population is php 2 250