ST 260-001_004 Test 3 Practice Questions - Fall 2023

ST 260-320 – EXAM 3 PRACTICE True/False 1) T F A Type I Error is the probability of rejecting the null hypothesis when it is actually true 2) T F If the underlying distribution of the variable of interest is normal, than we can assume that the distribution of sample means is also normal, regardless of the sample size. 3) T F If one does not know the Population Standard Deviation and must estimate it with the Sample Standard Deviation, then one should use a Z statistic instead of a t statistic when calculating confidence intervals. 4) T F As the level of confidence gets larger, the width of a confidence interval gets smaller. 5) T F The standard error of a sampling distribution where the population standard deviation is known is σ √ n 6) T F After an event occurs, the probability that that event was a success is either 0 (no success) or 1 (success). 7) T F A Scatterplot is a graph of 2 categorical variables 8) T F A correlation coefficient of 0 indicates a strong linear association between variables.** - you want it to be close to 1 or -1*** 9) T F The correlation coefficient ( r ) is a measure of ANY (linear, non- linear, quadratic, etc.) association between 2 variables 10) T F The correlation coefficient ( r )must be between 0 and 1 - ** must be between -1 and 1** r^2 is between 0 and 1 11) T F In Hypothesis Testing, we would reject the Null Hypothesis (H O ) when p >  - *** you reject when its LESS than alpha 12) T F A perfect NEGATIVE correlation would have a value of 1 13) T F High correlation indicates that one variable causes the changes in the other variable 1

Short Answer 14) What is the correlation coefficient of the following graph? ________r = -1.0, SSE=0 15) What would the correlation coefficient of the following graph be close to? ____r=0 _________ 16) What would the correlation coefficient of the following graph most likely be close to? ** WILL BE OBVIOUS – see obviously not negative, obviously not1 a) .20 b) -.20 c) 1.00 d) .85 2

18) The USDA is interested in knowing if the Tastes Good Peanut Company is really keeping to their claim of actually providing 50 lbs. of Peanuts in their “50 Pound Bag” that they sell to the general public. To test this, the auditor takes a sample of 100 bags of peanuts and calculates their mean weight. He finds from his sample of 100 bags that the Sample Mean weight is 49.8 lbs. and that the Sample Standard Deviation is 1.5 lbs. a) Calculate a 90% Confidence Interval around the mean.  USE T TABLE BC ST. DEV b) As the auditor, do you find this to be a plausible value to support that the company is putting at least 50 lbs of peanuts in their “50 Pound Bag” given the result of your confidence interval? State your conclusion in the language of the problem . c) If you were to use a 80% Confidence Level instead, would that change your decision? Why or why not? 4

19) Suppose a quality engineer working at the Scotts Mulch company is looking at the machine that fills the bags with mulch. For this machine, it should fill the bag with 25 pounds of mulch. Management has concerns that the machine may be off in filling the bags. To test, the quality engineer takes a sample of 36 bags and finds a sample mean weight for the bags to be 25.4 pounds. Suppose the population standard deviation (  ) is known to be 1.2 pounds. Use  =0.05. a) State the null and alternative hypotheses H0: M = 25 HA : M =/ 25 b) Calculate the appropriate test statistic Z = 25.4 -25/1.2sw rt of 36 = .4/.2 = 2 c) Calculate the appropriate p-value  Look at both directionds  P(z>2.0) +P(z<-2/0) d) What is your conclusion? Is the machine filling the bag with something other than 25 pounds of mulch? Why? 5

Statistical Formulae X = the value of x in which we are interested X = the (sample) mean μ = the (population) mean of the distribution s = the (sample) standard deviation σ = the (population) standard deviation of the distribution n = the sample size For Sampling Distributions (if n is sufficiently large or underlying distribution is Normal): E( X ) = μ x = μ σ X = σ √ n Z = X − μ σ √ n For choosing a sample of k items from a population of n items , ( n k ) − → n! k ! ( n − k ) ! Confidence Interval Limits for the Population Mean, σ known: X ±Z ( α 2 ) σ √ n Confidence Interval Limits for the Population Mean, σ unknown: X ±t ( α 2 ,n − 1 ) s √ n 7