practice questions solution

1. Bags of M&Ms have six different colors: red, orange, yellow, green, blue, and brown. We are interested to see if all six colors occur in equal proporAon. We take a simple random sample of 1000 candies: 111 are blue, 225 are orange, 300 are green, 189 are red, 80 are yellow, and 95 are brown. To test the hypotheses, we have: Ho: All of the colors occur in equal proporAon (1/6) Ha: At least one of the colors occurs with proporAon not equal to 1/6 What are the expected counts for each color of M&M? _________ 2. In order to correctly perform a Chi-squared test for Goodness of Fit, the categories must be: a) ordered b) mutually exclusive c) small d) conAnuous 3. The regression equaAon for predicAng cost of a flight was fiZed using the following data The regression line is determined to be: predicted cost = 0.21(distance) + 57.18 What is true about the predicted value of the cost of a flight of 50 miles? a) It is expressed as: 0.21(50) + 57.18 = $67 b) The predicted price would be very realisAc because some of the airfares were less than $90 c) It is not appropriate to predict the flight's cost because the distance is out of the range of the observed distances. d) It is less than $106 4. Give a range of probabiliAes for the event that a t-distributed variable with ten degrees of freedom has an absolute value greater than 2.5. Put each number in decimal format with three decimal places, for example "0.125". (And be sure to put them in the correct order - the lower bound should be first!) _____< p < _____ 166.67 1000 ㄨ 刘 166.67 chi Squared GOF is not appropriate for continuous data 0.01 0 o u d f 10 check the time 2228 ㄥ t L 2.764

5. Julia is studying the cocoon length of a certain type of buZerfly, she manages to find a simple random sample of 84 cocoons and creates a 95% confidence interval of their lengths. When interpreAng the interval, she writes, "There is a 95% chance that the populaAon mean length is between 3.3 and 4.2 cenAmeters." Which of the following statements is correct? a) This interpretaAon is incorrect because once a sample is taken, the confidence interval will either contain the parameter or it will not, without reference to chance. b) This interpretaAon is incorrect because a confidence interval should not be constructed when we have a simple random sample. c) This interpretaAon is incorrect because a confidence interval predicts the sample mean length, not the populaAon mean length. d) This interpretaAon is correct. 6. Ager conducAng an internal review, a company finds that the event of having an above- average score on the interview is independent of having an above-average performance on the job. Which of the following is true? a) Having an above-average performance on the job and an above-average interview are mutually exclusive. b) The probability of having both an above-average interview and an above-average performance on the job is equal to the product of each individual probability. c) The probability of having an above-average performance on the job changes when adding the condiAon of having an above-average interview. d) The probability of having an above-average interview or above-average performance on the job is equal to the sum of each individual probability. 7. What is the probability of a standard normal variable having a value between -0.5 and 2.5? _______. 8. Which of the following must always be true regarding the data set used to create the box plot below? a) the data is normally distributed b) the median is less than the mean c) the median is about 70 d) none of the above is true We use confidence intervalto predict Population meaninstead of samplemean A j B We denote two eventsto be A B mutually exclusive givesus PCA n BE o ou Pl At B PIA t Pl B P An BkPIAPl B defof independence Mutually exclusive two events cannotoccur at the same time Independent turn they canoccur at the same time Checking zone 0.6835 o 9938 o 3085 0.6835 Z 2.5 P o9938 z 0.5 p o 3085 The box plot will show if a statistical data set is symmetric or skewed. When the median is in the middle of the box, and the whiskers are about the same on both sides of the box, then the distribution is symmetric. Additionally, the normal is not the only symmetric distribution, others distributions could present this box plot.

13. Based on previous studies it seems that more than 10% of people who are registered voters in the city of Chicago do in fact vote when there is an elecAon. A simple random sample (SRS) of 500 registered voters in the city of Chicago was selected and discovered that 88 of them voted in the last elecAon. If a researcher runs a z-test for proporAons, what would be the appropriate standard error when compuAng the z-test? Show all your work to compute it. 14. Is there a relaAonship between liking tea and liking coffee? The following table shows data collected from a simple random sample of 100 adults. Each were asked if they liked coffee (yes or no) and if they liked tea (yes or no). a) State hypotheses. b) Check any necessary assumpAons and based on it define the appropriate test. c) Compute the test staAsAc. d) Compute the p-value. e) Conclude and interpret in context using a 5% significance level. SE proportion f 0 1X11 011 o 013 500 a Hoi liking tea and liking coffee are independent Hai ⼀ not independent b We have a SRS All EVs are greater than 5 andthe categories of variables aremutually exclusive appropriate to Use Chi squared Independence C EU like tea andlike a Heel 升 袋 22 EV liketeaand don't like a Hee 60 5 33 EU I don't like tea and like a Hee 40 怂 5 18 EV I dnt like tea and don't like coffee 60 个 怂 27 x ˋ 30 212 哈 叶 少 ⼗ if 10774 d d f 2 1 ㄨ 2 1 1 P o.net Our p valueis less than 005 so we reject the nun hypothesis We have enough evidence to say that liking tea and liking coffee are not independent

15. A track coach claims that their new month-long training program will reduce the mile Ame by more than 1 minute. You want to staAsAcally test the coach's claim. You decide to randomly select 5 runners and record their mile Ames. You then have them follow the coach's training program for a month and record their mile Ames post-training program. The Ames are listed below. a) What type of test is appropriate for this experiment set up? b) State the appropriate hypotheses. c) How many degrees of freedom are involved in this test? d) The test staAsAc was 4.42. Based on it, compute the p-value. e) State the conclusion in context using a 1% significance level. a paired test b Hoi meant before mean later 1 Ha meant before mean take 1 4 H 5 1 4 d o.oo5cpco.oobzsespco.no We can reject the hull hgpmu is we have enough eidenu to say the coach's claim is true