PSY 311 1st Edition Lecture 2Outline of Last Lecture I. Invasion of Space II. Ethics a. Who is Responsibility b. Utilitarianism and Rights III. Informed Consent Outline of Current Lecture I. Standard Deviation II. Z- Scores a. Z tables III. Sampling Distribution a. Standard errorIV. Hypothesis Testing (5 steps) a. Null hypothesisb. Alternative hypothesisV. Experimenters Decisiona. Type 1 error b. Type 2 error Current LectureStats review of PSY 310: Everything you should know I. Standard Deviation - Whatis is the sample standard deviation of 5,7,9,and 19First you have to find the mean of the sample by adding all the scores up from the sample. 5+7+9+19= 40 , 40/4= 10 your mean is 10. Then you find how many deviations is the sample scores from the mean by subtracting them. 5-10= -5, 7-10= -3, 9-10= -1, 19-10= 9 then you add all of the deviations up witch will give you 0.Next you have to find the sum of squares (SS) by squaring all the deviations scores and adding them all up (-5)²= 25, (-3)²= 9, (-1)²= 1 (9)²= 81 so the sum of squares equals 25+9+1+81= 116 These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Then you have to find the variance (s²) by diving the sum of squares by the degrees of freedom of the sample (n-1) SS/n-1 or 116/3 = 38.67 Lastly you find the standard deviation (s) by square rooting the variance which gives you 6.2 II. Z scores Z= (X-µ)/, = (X-µ)/z, X= µ+z(), µ= X-z() - If X=20, z= -.67 , and  = 12, what is µ You just plug the numbers into the equation µ= 20-(-.67)(12)= 28 - A student scores in 83 in an exam with a class mean of 74 and a class standard deviation of 15. The instructor transforms everybody’s score so that the NEW mean is 65 and the NEW standard deviation is 10. What will the student’s new score be?You have to find the Z score first by putting the numbers in the equation z= 83-74/15= 0.60 Then you use the transformation equation to find the new score which is New X= Newµ + z(new) therefore you get X= 65+(0.60)(10)= 71a. Z tables - If µ=30 and =8, what is the probability that a randomly selected score is lessthan 26 First you find the z score z= 26-30/8 = -0.5. Then the way that you would write the probability out is p< -0.5. After you do that you draw a normal distribution and place the Z score -0.5 on thedistribution and shade everything that is less than the Z score. Since a large portion is shaded you would go to the Z table and find the Z score -0.5 and locate the proportion of the body because the shaded area is large and it equals 0.3085. III. Sampling Distribution - What is it??Sampling distribution is a distribution of sampling means. A sampling distribution is normal if:- The original population is normal- If sample size is > 30 A sampling distribution uses:- The standard error instead of standard deviation- The mean for the original population is the same for the sample a. Standard Error- What is it ?The standard error is the standard deviation of the sampling distribution m= /n (Square root) A sampling distribution problem:- A sample of 25 people was drawn from a population with µ=45 and =10. What is the probability that the sample mean will be greater than 50?- use the formula Z= (M-µ)/ m First find the standard error which is m= /n which is 10/25 or 10/5=2. Then find the z score by plugging the numbers into the formula Z= (50 – 45)/2 = 2.5. Next write the probability out which is p (z>2.5) and draw your distribution. Place the Z score on the distribution and shade everything that is greater than 2.5. Then you will find the Z score on the Z table and look for the proportion of the tail because the shaded area is small which will give you 0.0062.IV. Hypothesis Testing (5 steps) Step 1 : State the hypotheses- Null hypothesis (H) states that in the general population there is no change- Alternative Hypothesis(H1) states that there is a change for the general population Step 2 : Determine the critical region - The most common critical region is = .05 Step 3 : Calculate the test statistic Step 4: Make a decision - Reject the null hypothesis: the treatment did have an effect - Fail to reject the null hypothesis: the treatment does not appear to have an effect. Step 5 : Report the statistic in APA style- The formate is Z= a number , p< or >alpha level - Use < if you reject the null hypothesis and > if you fail to reject the null hypothesisV. Experimenters Decision Actual SituationNo Effect, H0 true Effect exists, H0 falseReject H0 Type I error Decision correct Accept H0 Decision correct Type II error - Type I error occurs when a researcher concludes that a treatment does have an effect when, if fact, it has no effect. To reduce type I errors you can reduce your alpha level for example change the alpha level from .05 to .01 - A type II error means that the hypothesis test has failed to detect a real treatment effect.To reduce type II errors or Beta you can make the sample size larger, increase the alpha level for example change the alpha level from .01 to .05 and keep the standard