Sampling distribution of the mean worksheet with answers

Provide a response to the following questions.

Note: Each team member should compute the following questions and submit to the Learning Team forum. The team should then discuss each team member’s answers to ascertain the correct answer for each question. Once the team has answered all the questions, submit a finalized team worksheet.

1. On a standard measure of hearing ability, the mean is 300, and the standard deviation is 20. Provide the Z scores for persons whose raw scores are 340, 310, and 260. Provide the raw scores for persons whose Z scores on this test are 2.4, 1.5, and -4.5.

2. Using the unit normal table, find the proportion under the standard normal curve that lies in the tail for each of the following:

a. z = 1.00

b. z = -1.05

c. z = 0

d. z = 2.80

e. z = 1.96

3. Suppose the scores of architects on a particular creativity test are normally distributed. Using a normal curve table (pp. 477–480 of the text), what percentage of architects have Z scores

a. above .10?

b. below .10?

c. above .20?

d. below .20?

e. above 1.10?

f. below 1.10?

g. above -.10?

h. below -.10?

4. A statistics instructor wants to measure the effectiveness of his teaching skills in a class of 102 students (N = 102). He selects students by waiting at the door to the classroom prior to his lecture and pulling aside every third student to give him or her a questionnaire.

a. Is this sample design an example of random sampling? Explain.

b. Assuming that all students attend his class that day, how many students will the instructor select to complete his questionnaire?

5. Suppose you were going to conduct a survey of visitors to your campus. You want the survey to be as representative as possible.

a. How would you select the people to survey?

b. Why would that be your best method?

6. Explain the eight characteristics of a normal distribution. Explain why converting raw scores to z scores is helpful in understanding data.

7. Explain the concept of a sampling distribution. Identify three characteristics of the sampling distribution of the sample mean.

8. How is the alternate hypothesis related to the null hypothesis? Explain the difference between a one-tailed test and a two- tailed test.

9. What is the probability of rolling a 2 or a 7 on a six-sided dice? Please show the formula and the calculation.

10. Converting raw scores to z-scores Consider a distribution of raw scores with: Mean = 10, s.d., = 2. What is the z score for a raw score of 7 in this distribution. Please show the formula and your calculations.