Question

In: Math

A researcher selects a sample of 49 participants from a population with a mean of 12...

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean that is at least equal to the population mean? 0.50 equal to the probability of selecting a sample mean that is at most equal to the population mean all of the above none of the above

Solutions

Expert Solution

Solution :

It is given that a researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5.

To find the probability of selecting a sample mean that is at least equal to the population mean.

Since, , thus , we can assume that is Normally Distributed. That is ,

We know that if is a Normal RV , then the Sample Mean is also Normally distributed.

Thus, we can conclude that, the probability of selecting a sample mean that is atmost equal to the population mean is also = 0.5. So the Required Answers are :

Required Probability = 0.5
equal to the probability of selecting a sample mean that is at most equal to the population mean.

Thus , the Correct Option is (C) --- All of the Above ......................................... (Ans)

milcah answered 6 days ago

Next > < Previous

Related Solutions

A researcher selects a sample of 100 participants from a population with a mean of 38...

A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20. About 68% of the sample means in this sampling distribution should be between ______ and ______. Show your work

A researcher selects a sample of n=25 individuals from a population with a mean of μ=60...

A researcher selects a sample of n=25 individuals from a population with a mean of μ=60 and standard deviation of σ=10 and administers a treatment. The researcher predicts that the treatment will increase scores. Following the treatment, the average scores for this sample is M=65. 1. Using symbols, state the hypothesis for a one-tailed test. 2. Calculate the z-score and place this on a standardized normal distribution. 3. With a one-tail α=0.05, state the conclusion of these findings. 4. Calculate...

. A researcher selects a random sample of 10 persons from a population of truck drivers...

. A researcher selects a random sample of 10 persons from a population of truck drivers and gives them a driver’s aptitude test. Their scores are 22,3,14,8,11,5,18,13,12, and 12. (a) Find the estimated standard error of the mean. (b) Find the 95% confidence interval for the population mean.

Question 27 options: A researcher selects a sample of n = 25 from a normal population...

Question 27 options: A researcher selects a sample of n = 25 from a normal population with µ = 80 and σ = 20. If the treatment is expected to increase scores by 6 points, what is the power of a two-tailed hypothesis test using α = .05? Enter the result for each step below: Step 1: Enter the standard error, σM (enter a number with 5 decimal places using only the keys "0-9" and "."): Step 2: Enter the...

A random sample of 49 measurements from one population had a sample mean of 10, with...

A random sample of 49 measurements from one population had a sample mean of 10, with sample standard deviation 3. An independent random sample of 64 measurements from a second population had a sample mean of 12, with sample standard deviation 4. Test the claim that the population means are different. Use level of significance 0.01. (a) What distribution does the sample test statistic follow? Explain. (b) State the hypotheses. (c) Compute x1 2 x2 and the corresponding sample test...

A random sample of 49 measurements from one population had a sample mean of 16, with...

A random sample of 49 measurements from one population had a sample mean of 16, with sample standard deviation 3. An independent random sample of 64 measurements from a second population had a sample mean of 18, with sample standard deviation 4. Test the claim that the population means are different. Use level of significance 0.01. (a) What distribution does the sample test statistic follow? Explain. The standard normal. We assume that both population distributions are approximately normal with known...

From a normal population, a sample of 39 items is taken. The sample mean is 12...

From a normal population, a sample of 39 items is taken. The sample mean is 12 and the sample standard deviation is 2. Construct a 99% confidence interval for the population mean.

For a distribution, the sample mean is 96, standard deviation is 12, and number of participants...

For a distribution, the sample mean is 96, standard deviation is 12, and number of participants is 285. Please show all work. What is the relative frequency of scores between 80 and the mean? How many participants are expected to have scores that fall between 80 and the mean? What is the percentile of someone scoring 80? How many participants are expected to have scores that are above 80?

A random sample of n1 = 49 measurements from a population with population standard deviation σ1...

A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 5 had a sample mean of x1 = 8. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 6 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements: What distribution does the sample test statistic follow? Explain....

A random sample of 49 measurements from a population with population standard deviation σ1 = 3...

A random sample of 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 12. An independent random sample of 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 14. Test the claim that the population means are different. Use level of significance 0.01. (g) Find a 99% confidence interval for μ1 − μ2. (Round your answers to two decimal...

Subjects