Zhi plays a game in which she can purchase a ticket and it has several chances, or "catches" to win money. The table below shows the probability of winning at each stage, and how much money the ticket can win at each catch. Every time Zhi plays the game, her ticket is played through each catch, which means we can win money at each stage. Given the probabilities and payout values in this table, what is the expected value of Zhi's ticket? Catch 0 40% $1.00 Catch 1 45% $5.00 Catch 3 12% $10.00 Catch 4 3% $25.00 Zhi went to a blackjack table at the casino. At this table, the dealer is using one standard deck of 52 cards that has just been shuffled. Zhi knows that getting 21, a blackjack, is the best hand possible. She really likes when she is dealt an ace first. Before the second card is dealt Zhi wondered what her chances were of getting another ace if she did not get a face card. What is the probability that the second card is an Ace, given that it is not a face card? Enter your answer as a percent, rounded to the nearest whole number. Mark created a similar diagram from the previous season, and he wanted to look into the team's losses. In the Venn diagram, circle A shows wins and circle B shows games played on Wednesday nights. How many games did the team lose on a Wednesday? Mark went back to this session's results. Mark then looked at the games won and lost at the two locations where they played. He made a two-way table. What is the probability that the team lost a game if they played at Lincoln Park? Using the same table, what was the probability that the team played a game at Daryl Fields OR the team won a game? Another player had a 25% accuracy at making three-point shots. Mark thought it was reasonable that each attempt was independent and the probability stayed at 25% for this player. Using the geometric distribution, what is the probability that the player first makes a three-point goal on his third attempt? Switching over to baseball, Mark noticed that the probability that a certain player hit a home run in a single game is 0.165. Mark is interested in the variability of the number of home runs if this player plays 150 games. If Mark uses a binomial distribution to model the number of home runs, what is the variance for a total of 150 games? Tasha continued reading the study of the 20 top-selling cars and their weight and gas mileage. It told her that r = -0.82. For this data, the value of the coefficient of determination is __________. Tasha next considered how the speed of a car influences how much fuel it uses. She found a graph for four different compact cars at different speeds, from 20 to 70 mph. The value of r for this graph will be closest to (A) __________. The value of r 2 will be (B) __________ (high or low). The explanatory variable is (C) __________. To begin the chi-square test, Kathy asked Randy and Jeanette to show her the data. They told Kathy that the company claims that the distribution of each color is 20%. %( Color Counts Red 123 23% Yellow 145 27% Green 64 12% ) Orange 129 24% Purple 75 14% \"We can't use the chi-square test in every instance because there are certain assumptions and conditions that must be met,\" explained Kathy. \"The first thing I look at is to see if all the expected frequencies are greater than 5.\" The observed frequency for the color yellow is (A) __________, and its expected frequency is (B) __________. Jeanette worked as a graveyard ward clerk at her local hospital. In addition to processing patient records, one of her assigned duties was to keep the candy bowl full on the ward's main desk counter, a perk that was often enjoyed by both patients' families and the hospital floor nursing and physician staff. Jeanette purchased several large bags of wrapped FruityTooty candy each week from a nearby warehouse store. Each bag contained a mixture of cherry, grape, apple, lemon and orange flavors. One night, Randy, the unit's charge nurse, stopped by the desk to drop off some records for Jeanette. Reaching into the bowl for a piece of candy, Randy remarked, \"I really love the green, apple-flavored ones, but there always seems to be a lot of cherry and grape flavors. Is that because the cherry candies are so popular, or does the bag contain less green ones than the other colors?\" It was a slow night on the floor, and Randy and Jeanette were intrigued by the question. They decided to randomly pick a candy from a new bag Jeanette had stored, note it's color, and place it back in the bag. Which of the following two statements are true? The count of drawing an orange candy has a binomial distribution. The distribution of the count of picking a red candy cannot be modeled as approximately normal is they pick candies over 100 times. The distribution of the count of purple candies cannot be approximated with a normal distribution. The count of drawing a green candy is not a binomial distribution. The sample proportion of red candies has a binomial distribution. The distribution of the count of picking a yellow candy can be modeled as approximately normal if they pick candies 15 times. Jeanette and Randy wondered if there were more red candies than what the company claimed. They counted 14 red, 8 green, 10 yellow, 10 purple and 6 orange candies in total from the bag. They decided to look at FruityTooty's website to see if the bags of candy were intentionally filled with more red candies. \"Hey Randy,\" said Jeanette. \"I found a question on the company's website where someone had asked the very same question.\" She showed Randy the answer from the FruityTooty's marketing department, claiming that each flavor was given an equal distribution in the bags. \"If this statement is true,\" said Randy, \"the total of each color should be 20%, which is not what we found in our simple sample.\" Determine the correct null hypothesis and alternative hypothesis. When Randy was studying for his bachelor's degree in nursing, he had taken a statistics course. Jeanette seemed eager to understand the meaning of these statistics a little better, and it was a slow evening, so he spent some time explaining to Jeanette about the null hypothesis and the alternative hypothesis. \"Let's look at the green candies.\" explained Randy, \"The hypothesis would be that there is a lower proportion of green candies than 20%, and the null hypothesis is what the company maintains, which is the proportion of colors is equal, and that green is 20%.\" A type I error would be made if the null hypothesis is (A) __________, but it is actually (B) __________. A type II error would be made if the null hypothesis is (C) __________, but it is actually (D) __________. \"So now,\" Jeanette asked, \"we are approaching the point where we can begin to test the hypothesis, right? And, we want to avoid making a type II error. How do we do that, Randy?\" Randy can increase the power of the test by increasing either alpha, or the (A) __________. Alpha, , is equal to the probability of making a(n) (B) __________. \"Now that we've established a confidence interval,\" Randy explained, \"we're now ready to test our hypothesis. Look at the counts we recorded, Jeanette. How many red candies did we find in our 400-count sample? And, what did the FruityTooty company claim would be the population proportion of red candies?\" \"There were 92,\" said Jeanette, \"and the company said the proportion would be 20%.\" \"Okay. Then we have enough information to compute the z-test statistic,\" said Randy. \"Here we go.\" Using the formula and data provided in the problem, the value of the z-test statistic is __________. Going back to their count from their purchased bags, and using the red candies as an example, Randy showed Jeanette how to calculate a 90% confidence interval. %( Color Counts Red 110 20% Yellow 151 27% Green 71 13% Orange 135 25% Purple 83 15% ) Using a 90% confidence interval for the population proportion, what are the lower and upper values of the interval? Lower Value - Upper Value A. 0.228 B. 0.166 C.0.172 D.0.241 While Jeanette was waiting for Randy to complete his computations, a thought occurred to her. \"Randy,\" she asked. \"wouldn't it make sense to run this test at least another 20 times? Wouldn't that make our analysis much more accurate?\" \"Well, it could, but if we did this as many as 20 times on this population, we could end up with making the wrong conclusion about the null hypothesis at least once or twice, which would be considered a false positive result,\" explained Randy. \"In other words, due to sampling error, we could end up with results that appear to be statistically significant, when they actually are not.\" Which of the following two choices could result in invalid hypothesis test results? The sample size is less than 10% of the population. A significance level of 5% is chosen after calculating the p-value. The expected number of successes and failures are greater than 10. The sample is collected using a random method and is representative of the population. The null and alternative hypothesis are stated before performing a hypothesis test. Performing multiple tests on the same population. To begin the chi-square test, Kathy asked Randy and Jeanette to show her the data. They told Kathy that the company claims that the distribution of each color is 20%. %( Color Counts Red 123 23% Yellow 145 27% Green 64 12% Orange 129 24% Purple 75 14% ) \"We can't use the chi-square test in every instance because there are certain assumptions and conditions that must be met,\" explained Kathy. \"The first thing I look at is to see if all the expected frequencies are greater than 5.\" The observed frequency for the color yellow is (A) __________, and its expected frequency is (B) __________. Zhi plays a game in which she can purchase a ticket and it has several chances, or "catches" to win money. The table below shows the probability of winning at each stage, and how much money the ticket can win at each catch. Every time Zhi plays the game, her ticket is played through each catch, which means we can win money at each stage. Given the probabilities and payout values in this table, what is the expected value of Zhi's ticket? Catch 0 40% $1.00 Catch 1 45% $5.00 Catch 3 12% $10.00 Catch 4 3% $25.00 Zhi went to a blackjack table at the casino. At this table, the dealer is using one standard deck of 52 cards that has just been shuffled. Zhi knows that getting 21, a blackjack, is the best hand possible. She really likes when she is dealt an ace first. Before the second card is dealt Zhi wondered what her chances were of getting another ace if she did not get a face card. What is the probability that the second card is an Ace, given that it is not a face card? Enter your answer as a percent, rounded to the nearest whole number. Mark created a similar diagram from the previous season, and he wanted to look into the team's losses. In the Venn diagram, circle A shows wins and circle B shows games played on Wednesday nights. How many games did the team lose on a Wednesday? Mark went back to this session's results. Mark then looked at the games won and lost at the two locations where they played. He made a two-way table. What is the probability that the team lost a game if they played at Lincoln Park? Using the same table, what was the probability that the team played a game at Daryl Fields OR the team won a game? Another player had a 25% accuracy at making three-point shots. Mark thought it was reasonable that each attempt was independent and the probability stayed at 25% for this player. Using the geometric distribution, what is the probability that the player first makes a three-point goal on his third attempt? Switching over to baseball, Mark noticed that the probability that a certain player hit a home run in a single game is 0.165. Mark is interested in the variability of the number of home runs if this player plays 150 games. If Mark uses a binomial distribution to model the number of home runs, what is the variance for a total of 150 games? Tasha continued reading the study of the 20 top-selling cars and their weight and gas mileage. It told her that r = -0.82. For this data, the value of the coefficient of determination is __________. Tasha next considered how the speed of a car influences how much fuel it uses. She found a graph for four different compact cars at different speeds, from 20 to 70 mph. The value of r for this graph will be closest to (A) __________. The value of r2 will be (B) __________ (high or low). The explanatory variable is (C) __________. To begin the chi-square test, Kathy asked Randy and Jeanette to show her the data. They told Kathy that the company claims that the distribution of each color is 20%. Color Counts %( Red 123 23% Yellow 145 27% Green 64 12% ) Orange 129 24% Purple 75 14% \"We can't use the chi-square test in every instance because there are certain assumptions and conditions that must be met,\" explained Kathy. \"The first thing I look at is to see if all the expected frequencies are greater than 5.\" The observed frequency for the color yellow is (A) __________, and its expected frequency is (B) __________. Jeanette worked as a graveyard ward clerk at her local hospital. In addition to processing patient records, one of her assigned duties was to keep the candy bowl full on the ward's main desk counter, a perk that was often enjoyed by both patients' families and the hospital floor nursing and physician staff. Jeanette purchased several large bags of wrapped FruityTooty candy each week from a nearby warehouse store. Each bag contained a mixture of cherry, grape, apple, lemon and orange flavors. One night, Randy, the unit's charge nurse, stopped by the desk to drop off some records for Jeanette. Reaching into the bowl for a piece of candy, Randy remarked, \"I really love the green, apple-flavored ones, but there always seems to be a lot of cherry and grape flavors. Is that because the cherry candies are so popular, or does the bag contain less green ones than the other colors?\" It was a slow night on the floor, and Randy and Jeanette were intrigued by the question. They decided to randomly pick a candy from a new bag Jeanette had stored, note it's color, and place it back in the bag. Which of the following two statements are true? The count of drawing an orange candy has a binomial distribution. The distribution of the count of picking a red candy cannot be modeled as approximately normal is they pick candies over 100 times. The distribution of the count of purple candies cannot be approximated with a normal distribution. The count of drawing a green candy is not a binomial distribution. The sample proportion of red candies has a binomial distribution. The distribution of the count of picking a yellow candy can be modeled as approximately normal if they pick candies 15 times. Jeanette and Randy wondered if there were more red candies than what the company claimed. They counted 14 red, 8 green, 10 yellow, 10 purple and 6 orange candies in total from the bag. They decided to look at FruityTooty's website to see if the bags of candy were intentionally filled with more red candies. \"Hey Randy,\" said Jeanette. \"I found a question on the company's website where someone had asked the very same question.\" She showed Randy the answer from the FruityTooty's marketing department, claiming that each flavor was given an equal distribution in the bags. \"If this statement is true,\" said Randy, \"the total of each color should be 20%, which is not what we found in our simple sample.\" Determine the correct null hypothesis and alternative hypothesis. When Randy was studying for his bachelor's degree in nursing, he had taken a statistics course. Jeanette seemed eager to understand the meaning of these statistics a little better, and it was a slow evening, so he spent some time explaining to Jeanette about the null hypothesis and the alternative hypothesis. \"Let's look at the green candies.\" explained Randy, \"The hypothesis would be that there is a lower proportion of green candies than 20%, and the null hypothesis is what the company maintains, which is the proportion of colors is equal, and that green is 20%.\" A type I error would be made if the null hypothesis is (A) __________, but it is actually (B) __________. A type II error would be made if the null hypothesis is (C) __________, but it is actually (D) __________. \"So now,\" Jeanette asked, \"we are approaching the point where we can begin to test the hypothesis, right? And, we want to avoid making a type II error. How do we do that, Randy?\" Randy can increase the power of the test by increasing either alpha, or the (A) __________. Alpha, , is equal to the probability of making a(n) (B) __________. \"Now that we've established a confidence interval,\" Randy explained, \"we're now ready to test our hypothesis. Look at the counts we recorded, Jeanette. How many red candies did we find in our 400-count sample? And, what did the FruityTooty company claim would be the population proportion of red candies?\" \"There were 92,\" said Jeanette, \"and the company said the proportion would be 20%.\" \"Okay. Then we have enough information to compute the z-test statistic,\" said Randy. \"Here we go.\" Using the formula and data provided in the problem, the value of the z-test statistic is __________. Going back to their count from their purchased bags, and using the red candies as an example, Randy showed Jeanette how to calculate a 90% confidence interval. Color Counts %( Red 110 20% Yellow 151 27% Green 71 13% Orange 135 25% Purple 83 15% ) Using a 90% confidence interval for the population proportion, what are the lower and upper values of the interval? Lower Value - Upper Value A. 0.228 B. 0.166 C.0.172 D.0.241 While Jeanette was waiting for Randy to complete his computations, a thought occurred to her. \"Randy,\" she asked. \"wouldn't it make sense to run this test at least another 20 times? Wouldn't that make our analysis much more accurate?\" \"Well, it could, but if we did this as many as 20 times on this population, we could end up with making the wrong conclusion about the null hypothesis at least once or twice, which would be considered a false positive result,\" explained Randy. \"In other words, due to sampling error, we could end up with results that appear to be statistically significant, when they actually are not.\" Which of the following two choices could result in invalid hypothesis test results? The sample size is less than 10% of the population. A significance level of 5% is chosen after calculating the p-value. The expected number of successes and failures are greater than 10. The sample is collected using a random method and is representative of the population. The null and alternative hypothesis are stated before performing a hypothesis test. Performing multiple tests on the same population. To begin the chi-square test, Kathy asked Randy and Jeanette to show her the data. They told Kathy that the company claims that the distribution of each color is 20%. Color Counts %( ) Red 123 23% Yellow 145 27% Green 64 12% Orange 129 24% Purple 75 14% \"We can't use the chi-square test in every instance because there are certain assumptions and conditions that must be met,\" explained Kathy. \"The first thing I look at is to see if all the expected frequencies are greater than 5.\" The observed frequency for the color yellow is (A) __________, and its expected frequency is (B) __________