Quiz 1

1.2.13​Hope the dog​Suppose you are testing to see if your dog, Hope, understands pointing towards an object. You put Hope through 20 trials and 12 times (or 60%) she goes to the correct object when given a choice between two objects. You then conduct a test of significance and generate the following 100 simulations using an applet.​Probability of heads: 0.5Number of tosses: 20Number of repetitions: 100Total = 100

Null: The long-run proportion of times Hope will go to the correct object is 0.50,​Alt: The long-run proportion of times that Hope will go to the correct object is more than 0.50 p=.5, p>.5 0.23 (23 dots are 0.60 or larger) No, the approximate p-value is 0.23, which provides little to no evidence that Hope understands pointing. .7 one possible value of the proportion of times Hope goes to the correct object out of 20 if she goes to the correct object 50% of the time in the long run

Question 2 P.1.15Suppose that the observational units in a statistical study are purchases made on a particular website (think of amazon.com) for one month.​

Part 1 whether or not they purchased a particular item whether or not they viewed a particular item purchaser's gender Part 2: price of items purchased purchaser's age shipping costs for items purchased

Right or leftMost people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGüntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13-70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.​

Right =,> .645 3.22 The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations above the null hypothesized value of 0.50. We have strong evidence that the proportion of couples that lean their heads to the right while kissing is more than 50%.

Question 1 P.1.10​In August of 2005, researchers for the American Society for Microbiology and the Soap and Detergent Association monitored the behavior of more than 6,300 users of public restrooms. They observed people in public venues such as Turner Field in Atlanta and Grand Central Station in New York City. For each person they kept track of the person's sex and whether or not the person washed his or her hands along with the person's location.

Gender, Washed Hands, And Location Yes No

Question 4 P.3.4Answer this question for each of the following statements: Which of the following explains what it means to say "the probability of ..." while describing the random process that is repeated over and over again?

If you repeatedly draw M&Ms at random a very large number of times, in the long-run 20% of those M&Ms will be red. If you repeatedly play the lottery a very large number of times, in the long run, you will win 0.1% of the times you play. If you repeatedly record whether or not it rains for a large number of days with the same weather conditions as tomorrow, in the long run you will see rain on 30% of such days. If you repeatedly select an adult American at random a large number of times, in the long run, roughly 30% of the time the selected adult will vote to get rid of the penny. True

LeBron James of the Miami Heat hit 765 of his 1354 field goal attempts in the 2012/2013 season for a shooting percentage of 56.5%. Over the lifetime of LeBron's career, can we say he is more likely than not to make a field goal?​

LeBron's long-run proportion of making a field goal statistic 50% Flip a coin 1354 times and record the number of heads. Repeat this 1000 times, keeping track of the number of heads in each set of 1354. Approximately ½ of 1354 (677) will be one of the most likely values since we assume the chance model is true.

1.2.22Spinning a coinIt has been stated that spinning a coin on a table will result in it landing heads side up fewer than 50% of the time in the long run. One of the authors tested this by spinning a penny 50 times on a table and it landed heads side up 21 times. A test of significance was then conducted with the following hypotheses:​H0: π = 0.50, Ha: π < 0.50​.

heads The p-value is 0.16; there is little to no evidence that a spun penny lands heads up less than 50% of the time. Null would be the same, alternative would be > 0.5. To calculate the p-value, find the probability that 29 or larger (58% or larger) occurred.

P.2.6In the 2012 National Football League (NFL) season, the first three weeks' games were played with replacement referees because of a labor dispute between the NFL and its regular referees. Many fans and players were concerned with the quality of the replacement referees' performance. We could examine whether data might reveal any differences between the three weeks' games played with replacement referees and the next three weeks' games that were played with regular referees. The pair of dotplots shown display data on the total number of penalties called in the game, again separated by the type of referee. Select all the statements below which might reveal whether the two types of referees differ with regard to the distributions of this variable.

-Both distributions are fairly symmetric, centered around 12 penalties, with a minimum of 4 penalties and a maximum of 24-25 penalties. -The games with 23-25 penalties are a bit unusual for both types of referees, with a few more of these extreme games for the replacement referees. -The game that had the highest number of penalties assessed was officiated by a regular referee.

1.3.22Choosing numbersUse the following information to answer the next questions.​ It has been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.​To investigate this, a professor collected data in her class. Here is the table of responses from her students:​

The long-run proportion of people that choose the number 3 null: pi=, alternative: pi> .42 The mean = 0.248 and SD = 0.076. The number of standard deviations the observed proportion is above 0.25 in the null distribution. We have strong evidence that the long-run proportion of people who will pick the number 3 is greater than 25%

P.3.6Suppose that baseball team A is better than baseball team B. Team A is enough better that it has a 2/3 probability of beating team B in any one game, and this probability remains the same for each game, regardless of the outcomes of previous games. Suppose that team A and team B play a best-of-three series, meaning that the first team to win two games wins the series.

part 1: It would be preferable for team A to play the best-of-three series, because in the longer series there is less of a chance for a weaker team to achieve the upset win multiple times. Part 2: Let rolls 1 and 2 represent team B winning a game and 3-6 represent team A. Roll the die and record who wins the game until one team has won two games (two or three times). Part 3: Let rolls 1 and 2 represent team B winning a game and 3-6 represent team A. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation a large number of times (say 1000) and record how often team A wins divided by the number of repetitions. Part 4: If teams A and B repeatedly play a best-of-three series, then in the long run team A will win 74.1% of those Team A has a higher chance of winning the best of three series than the 2/3 chance of winning any one game).