Statistics and Probability Answers

A certain population is composed of the numbers 4, 5, 6 and 7. What is the mean of the sampling distribution of the sample mean if each sample contains two elements?

The mean of the sample means in a sampling distribution is 2.6. What is the mean of the population from which the scores are sampled?

How many possible samples of size n = 3 can be drawn from a population of size 10? *

The head of the Philippine University (PU) observes a decline on the alcoholic expenditures of learners from a monthly expenditure of Php 350 pesos in the previous year. To check on this, he randomly selected 10 PU learners who drink alcoholic beverages and asked the amount, in pesos, that they usually spend on alcoholic beverages in a month. It is known that the usual amount spent on alcoholic beverages by learners who drink alcoholic beverages follows the normal distribution with standard deviation of Php 10. The data collected are: 400, 235, 200, 250, 200, 300, 500, 430, 420, and 220.

Construct and interpret a 95% confidence interval for the true mean amount spent by the learners on alcoholic beverages.

Find a 90% confidence interval for the true mean amount spent by the learners on alcoholic beverages.

The leader of the association of jeepney drivers claims that the average daily take home pay for all jeepney drivers in Baguio City is 400 pesos. A random sample of 100 jeepney drivers in Baguio City was interviewed and the average daily take home pay of these drivers is found to be 425 pesos. Use a 0.05 significance level to find out if the average daily take home pay of all jeepney drivers in Baguio City is different from 400 pesos. Assume that the population variance is 92 pesos.

According to one of the teachers in your school, the senior high school students sleep for 7 hours a day on a weekday. You wanted to prove this claim by making a survey of 50 senior high school students. You will be asking the students about how long they sleep in a regular weekday. Record the results of your survey. As a researcher, you need to compute the mean and standard deviation of your sample.

Create a 90%, 95%, and 99% confidence interval for the mean time of sleep for senior high school students. In your report, the raw data should be present, and the computation should be complete

If a population has a variance of 6.4, what is the variance of the sampling distribution of it's means? The sampling distribution has a sample size of 2 and all possible samples are drawn with replacement

Random samples of size N=2 are drawn from a finite population consisting of the number 5,6,7,8, and 9. Compute for the mean, Variance,and Standard deviation, and also the mean, Variance, and the Standard deviation of the sample mean

II – Answer each of the following questions. Use extra sheets if necessary.

1. Consider the population consisting of the values (4, 6, 8).

a. List down all the possible samples of size 2 with replacement.

b. Compute the mean of each sample.

c. Compute the mean of the sampling distribution of means.

d. Identify the probability of each sample.

e. Compute the population mean.

f. Compare the population mean with the mean of the sampling distribution of means.