Cumulative Exam — Cumulative exam Answers

In a statistics activity, students are asked to spin a penny and a dime and determine the proportion of times that each lands with tails up. The students believe that since a dime is lighter, it will have a lower proportion of times landing tails up compared with the penny. The students are instructed to spin the penny and the dime 30 times and record the number of times each lands tails up. For one student, the penny lands tails side up 18 times, and the dime lands tails side up 20 times. Let pD = the true proportion of times a dime will land tails up and pP = the true proportion of times a penny will land tails up. The P-value for this significance test is 0.296. Which of the following is the correct conclusion for this test of the hypotheses at the level?

According to a recent survey of adults, approximately 62% carry cash on a regular basis. The adults were also asked if they have children. Of the 46% who have children, 85% carry cash on a regular basis. Is carrying cash independent from having children in this sample?

There are 4 blood types, and not all are equally likely to be in blood banks. 49% of donations are type O blood, 27% of donations are type A blood, 20% of donations are type B blood, and 4% of donations are type AB blood. A person with type A blood can safely receive blood transfusions of type O and type A blood. If three donations are made, what is the probability that at least 1 of them can be safely used in a blood transfusion on someone with type A blood?

At a carnival game, the chance of winning a prize is 0.45. Kylee plays the game 3 times. Using the table, what is the probability that she wins at least 1 prize?

A 95% confidence interval for the true proportion of teenagers who have been to a professional sporting event is (0.289, 0.416). Is it reasonable to believe that more than 25% of teenagers have been to a professional sporting event?

A ski resort claims that there is a 75% chance of snow on any given day in January and that snowfall happens independently from one day to the next. A family plans a four-day trip to this ski resort in January. Let X represent the number of days it snows while the family is there. What are the mean and standard deviation of X?

The times to pop a 3.4-ounce bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. A random sample of four bags is selected and the mean time to pop the bags is recorded. Which of the following describes the sampling distribution of all possible samples of size four?

A local charity holds a carnival to raise money. In one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces marked with the values 0, 1, 2, 5, and 10. The participant wins the dollar amount marked on the space on which the wheel stops. Let X represent the value of a spin. The distribution of X is given in the table.What is the median of the distribution?

Based upon historical data, it is known that 8% of 12-egg cartons contain at least one broken egg. A grocery store manager would like to carry out a simulation to estimate the number of cartons, in a sample of 10, that would contain at least one broken egg. She assigns the digits to the outcomes.01-08 = carton contains a broken egg09-99, 00 = carton does not contain a broken eggHere is a portion of a random number table.In the first trial, line 1, 1 of the first 10 double-digit numbers is between 01 and 08, meaning that 1 of the 10 cartons of eggs contains at least one broken egg. Starting at line 2 and using a new line for each trial, carry out 4 more trials. Based on the 5 trials, how many cartons of eggs out of 10 cartons are expected to contain at least one broken egg, on average?

A carnival game is designed so that approximately 10% of players will win a large prize. If there is evidence that the percentage differs significantly from this target, then adjustments will be made to the game. To investigate, a random sample of 100 players is selected from the large population of all players. Of these players, 19 win a large prize. The question of interest is whether the data provide convincing evidence that the true proportion of players who win this game differs from 0.10. The computer output gives the results of a z-test for one proportion.Test and CI for One ProportionTest of p = 0.1 vs p ≠ 0.1Sample1X19N100Sample p0.1995% CI(0.113, 0.267)Z-Value3.00P-value0.0027

A student believes that a certain 6-sided number cube, with the numbers 1 to 6, is unfair and is more likely to land with a 6 facing up. The student rolls the cube 100 times and lands with 6 facing up 20 times. The P-value for the test of the hypotheses, H0:p=0.17 and Ha:p>0.17, is 0.19. What is the correct conclusion given a=0.05?

The proportion of all US adults who eat popcorn when they go to the movie theater is p = 0.87. A random sample of 20 US adults was selected and asked if they eat popcorn when they go to the movie theater. Which of the following is the shape of the sampling distribution of ?

A major car dealership has several stores in a big city. The owner wants to determine if there is a difference in the proportion of SUVs that are sold at stores A and B. The owner gathers the sales records for each store from the past year. A random sample of 55 receipts from store A shows that 30 of the sales were for SUVs. Another random sample of 60 receipts from store B shows that 42 of the sales were for SUVs. Assuming conditions for inference are met, what is the 99% confidence interval for the difference in proportions of sales that are SUVs?Find the z-table here.

Student body elections are coming up and there are a lot of options. There are 3 candidates for president, 4 for secretary, and 10 for mascot. Suppose a student were to fill out their ballot by randomly picking a candidate or abstaining for each position. Each outcome in the sample space for the random ballots is equally likely. What is the probability of each outcome in the sample space?

A student would like to estimate the proportion of students at his school who have lunch during period 4. To do so, he selects a random sample of 40 students and finds that 30% of them have period 4 lunch. Later, he goes to the guidance office and finds that of the 380 students at this school, 25% of them have period 4 lunch. Which of the following properly describes the number, 25%?

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The range of the distribution of ages is 3. The table displays all possible samples of size 2 and the corresponding ranges for each sample.Using the values in the table, is the sample range an unbiased estimator?

A nontraditional deck of cards has 30 total cards: 5 hearts, 10 clubs, 8 spades, and 7 diamonds. The cards are shuffled, and the top card is noted. This process is repeated 100 times. What is the probability the top card is spades in more than 30% of the sample?Find the z-table here.

In early 2019, the US rate of recycling plastic water bottles was only 23%. A government agency designs an expensive program to increase the recycling rate. The program will be tested in Texas and, if successful, it will be used nationally. A hypothesis test is conducted with H0: The proportion of water bottles that are recycled is still 23% after the program, and Ha: The proportion of water bottles that are recycled is more than 23% after the program. What is a Type II error and its consequence in this context?

An English test has 50 multiple-choice questions, each with five answer choices and one correct answer. A student guesses each answer choice randomly. Let X represent the number of questions answered correctly. What is the shape of the probability histogram of X?

In a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. The students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. For one student, it lands tails side up six times. The student will construct a 90% confidence interval for the true proportion of tails up. Are the conditions for inference met?