Answer All Question And Show All Work. Psychology Essay

DOUBLE SPACE STATISTICS do homework --homework -6 problems( 6 , 7 , 9 , 10 , 13 15 , 17 , 18 , 19 , 21 , 23 , 25 ) , homework 7 problems ( 1, 5 , 6 , 7 , 11, 18 , 22 , 25 , 26 )

Key Termsbell-shaped distribution fixed event
Gaussian distribution normal distribution probabilityrandom event sample space
standard normal distribution standard normal transformation symmetrical distributionunit normal table /distribution /score /table
z transformation• • End-of-Chapter Problems tual Problems
Describe in words how to compute plx).
State two characteristics of a probability.
' The normal distribution is symmetrical. What does this mean?
4. What type of distribution is most commonly applied to behavioral research?
5. A normal distribution has a mean of 0 and a standard deviation of -1.0. Is this possible? Explain.6. What are the values of the mean and the standard deviation in the standard normal distribution?
7. What is a z score?
8. State the standard normal transformation formula in words.
9. What are two steps to locate proportions under the normal curve'7
10. What are two steps to locate the cutoff score for a given proportion?

hypothetical population consists of eight individuals ages 13, H, 17, 20, 21, 22, 24, and 30 years.
(a) What is the probability that a person in this population is a teenager9 lb) What is the probability of selecting a participant who is at least 20 years old?
(c) What is the probability of selecting a participant older than 30?
12. On the basis of statistics from the previous
I 3 years, a maternity ward states that 97% of patients say they are satisfied with their birthing experience. If 100.000 patients gave birth in that maternity ward over the previous 3 years.
I then how many patients do we expect were not satisfied with their visit?
p. Using the unit normal table, find the proportion under the standard normal curve that lies to the right of each of the following:(a) z* 1.00
(b) z—1.05 Ic) z = -2.80
(d) z = 0
le) z*= 1.96
14. Using the unit normal table, find the proportion under the standard normal curve that lies to the left of each of the following:
(al z = 0.50
(b) z—1.32
(c) z = 0
Id) z« -1.96 le) z*-0.10
15. Using the unit normal table, find the proportion under the standard normal curve that lies between each of the following:
(a) The mean and z»0 (bl The mean and z= 1.96

Icl /»-1.50and/« 1.50 Id) / *-0.30 and /■ -0.10 (el *= 1.00 and r- 2.00
M6. State whether the first area is bigger, the sec*, 'ond area is bigger, or the two areas are equal | in each of the following situations:
lal The area to the left of t = 1 00 and the area to the right of /«-1 00 Ibl The area to the left of/«100 and the area to the left of / • -1 00 Icl The area between the mean and z- 1.20 and the area to the right of z - 0 80 (d) The area to the left of the mean and the area between / • ±1.00 lei The area to the right of z = 1.65 and the area to the right of/--1.65
llt/'An athletics coach states that player run times (in seconds! for a 100-meter dash are normally distributed with a mean equal to 0.12 and a standard deviation equal to 0.02 second. What percentage of players on the team run the 100-meter dash in O.U seconds or faster (i.e., in less timel?
/18. State the z score that is the cutoff for each of \ ^ the following:
^4al The top 5% of scores
Ibl The bottom 2.5% Of scores
(c) The top 69.5% of scores
Idl The top 50% of scores
lei The bottom 50% of scores
19 A sample of final exam scores is normally dis-'''tribuled with a mean equal to 20 and a variance equal to 25.
lal What percentage of scores is between 15 inrfWf
Ibl What raw score is the cutoff for the top 10% of scores?
Icl What is the probability of a score less than 27?
Idl What is the proportion below 13?
20. A college administrator states that the average hiqh school GPA for incoming freshmanequal to 3 30 and a standard deviation equal to 0.20. If students with a GPA in the top 10% will be offered a scholarship, then what is the minimum GPA required to receive the scholarship?
21. 4 set of scores measuring aggression is nor-illy distributed with a mean equal to 23 and
a standard deviation equal to 2.5. Find the proportion:
lal To the left of k ■ 19.0
(bl To the right of x ■ 25 5
(cl Between the mean and * ■ 19.0
Idl To the left of n ■ 25.5
lei To the right of *■ 19.0
22. A set of data is normally distributed with a mean of 3.5 and a standard deviation of 0.6. State whether the first area is bigger, the second area is bigger, or the two areas are equal in each of the following situations for these data:
lal The area above the mean and the area below the mean Ibl The area between 2.9 and 4.1 and the area between 3.5 and 4.7 Icl The area between the mean and 3.5 and the area above 5.3 (dl The area below 3.6 and the area above 3.4 (el The area between 4.1 and 4.7 and the area between 2.9 and 3.5
23. A normal distribution has a mean equal to 45. What is the standard deviation of this normal distribution if 2.5% of the proportion under the curve lies to the right of * = 50.88?
24. A normal distribution has a mean equal to 10. What is the standard deviation of this normal distribution if the cutoff for the top 5% is *-12.47-»2 A no, J*QU*normal distribution has a standard deviation I to 10. What is the mean of this normal distribution if the probability of sconng below x-IOrs 5000’26. A normal distribution has a standard deviation equal to 32. What is the mean of this normal distribution if the probability of scorinq above

central limit theorem (aw of (a rge numbers sample designsampling distribution sampling error sampling with replacementsampling without replacement
standard error
standard error of the mean• • • End-of-Chapter Problems Factual Problems
t. What is a sampling distribution?
2. Explain how conditional probabilities are related to sampling without replacement.
3. Distinguish between sampling with replacement and sampling without replacement.
4. Distinguish between sampling where order matters and sampling where order does not matter.
5. The sample mean is an unbiased estimator of the population mean. Explain this statement.
6. Define the central limit theorem.
7. Explain why the following statement is true-M-Un-
Concept and Application Problems
13. 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.
la) Is this sample design an example of random sampling'’ Explain.
lb) Assuming that all students attend his class that day. how many students will he select to complete the questionnaire?
14. A local high school is interested in studying how teacher perceptions of students, as being intelligent or not. affect the success8. Can the mean of a sampling distribution be a negative value? Explain.
9. The sampling distribution of the sample mean approximates the shape of what type of distribution?
10. What values do you need to know to compute the formula for standard error’
11. The standard error measure is the standard deviation for what type of distribution?
12. How would the standard error change if (a) the population standard deviation increased and (b) the sample size increased?of freshman students in the classroom. The school creates an Excel spreadsheet listing all freshman students in alphabetical order and places their names into one of two columns. All students listed in the second column are selected to participate in this study. Is this sample design an example of random sampling? Explain.
15. A support group has 12 patients who attend each week. Suppose 3 patients are selected at random to participate in a study. How many different samples of this size can be selected from this population of 12 patients using la) experimental sampling and lb) theoretical sampling?

16. Using the theoretical sampling strategy, how many samples of size 4 |ft ■ 4) can be drawn from a population of size:
(a) N-5? Ibl N- 8? |c) N=16? Id) A/-5(P
17. Using the experimental sampling strategy, how many samples of size 3 In ■ 31 can be drawn from a population of size:
la) N = 5? lb) N = 6? Ic) N = 7? Id) N-8?
18. The sample mean is an unbiased estimator of the population mean. What do we expect the sample mean to be equal to when the population mean is equal to:
la) (i-87 lb) |i-0? Id|i «207
Id) n = oo? le) h = -40? If) |t = 003?
19. Using the central limit theorem, what is the distribution of sample means when the population distribution it:
la) rectangular'» lb) normal?
Ic) positrvely skewed9 Id) nonmodal?
(•) multimodal?
If) negatively skewed7
20 State whether each of the following statements it true or false. If false, then explain what would make the statement true.
fa! The central limit theorem explains why the mean is always at the center of a distribution, lb) The standard error of the mean if the standard deviation of a sampling distribution of sample means Ic) The mean of a sampling distribution is equal to the population mean from which samples are selected.
21. State whether each of the following statements concerning the sample mean is true or _talc» If false then explain what would makeId There is more than a 5% probability of selecting a sample mean that is farther than 2 S£M from the population mean.
Id) The sampling distribution of sample means is approximately normally distributed.
22. A population with a positively skewed distribution of scores has a mean of 5 and a standard deviation of 4.
la) What is the shape of the sampling distribution of the mean for this population?
Ibl What is the mean of the sampling distribution for this population?
Ic) Suppose a researcher selects two samples from this population and records a sample mean of 3 5 in each sample. If Sample A if ft ■ 12 and Sample B if ft ■ 20. in which sample will a sample mean of 3.5 be less likely? Explain.
23. A population is normally diftnbuted with a mean of 56 and a standard deviation of 12.
la) What if the mean of the sampling distribution ||ij for thif population?
Ibl If a sample of 36 participants if selected from this population, what if the ftandard error of the mean lo^?
(c) Sketch the shape of this distribution with M±3S£M.
24. A population if normally diftnbuted with a mean of -30 and a standard deviation o» 4.
(a) What is the mean of the sampling distribution IhJ for this population?
Ibl If a sample of 16 participants if selected from this population, what is the standard error of the mean loj?
Ic) Sketch the shape of this distribution with M±3S£M.
25 A population of scores is normally distributed with a standard deviation equal to 7. State