Cumulative Exam — Cumulative exam Answers

From previous experience, the owner of an apple orchard knows that the mean weight of Gala apples is 140 grams. There has been more precipitation than usual this year, and the owner believes the weights of the apples will be heavier than usual. The owner takes a random sample of 30 apples and records their weights. The mean weight of the sample is 144 grams with a standard deviation of 13.2 grams. A significance test at an alpha level of produces a P-value of 0.054. What is the correct interpretation of the P-value?

A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Four cards are drawn from the deck at random.What is the approximate probability that exactly three of the cards are diamonds?

A random sample of 30 professional tennis players is selected. For each tennis player, their first serve percentage and their second serve percentage are recorded. A 95% confidence interval for the mean difference (first – second) in serve percentages is found to be 0.10 to 0.18. A tennis coach claims that there is no difference in first and second serve percentages among professional tennis players. Is this claim supported by the confidence interval?

A medical clinic is randomly selecting three staff members to attend a conference. The clinic employees include 7 nurses, 3 doctors, and 4 office staff. What is the probability that three nurses are selected to attend the conference?

Marleny is creating a game of chance for her family. She has 5 different colored marbles in a bag: blue, red, yellow, white, and black. She decided that blue is the winning color. If a player chooses any other color, they lose 2 points. How many points should the blue marble be worth for the game to be fair?

The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class.

A study is done to estimate the true mean satisfaction rating for all customers of a particular retail store. A random sample of 200 customers is selected and a 99% confidence interval for the true mean satisfaction rating is 7.8 to 8.4 where 1 represents very dissatisfied and 10 represents completely satisfied. Based upon this interval, what conclusion should be made about the hypotheses: = 8 versus 8 where μ = the true mean satisfaction rating for all customers of this store at α = 0.01?

A conference consists of 5 sessions: A, B, C, D, and E. Here are the costs of the sessions.Session A: $50Session B: $50Session C: $100Session D: $150Session E: $200A participant plans to attend 3 sessions. Here is a list of all possible samples of size 3 sessions from this population of 5 sessions: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, and CDE. Which of the following gives the sampling distribution of the sample minimum session price for samples of size 3, selected from the population of these 5 sessions without replacement?

A school guidance counselor is concerned that a greater proportion of high school students are working part-time jobs during the school year than a decade ago. A decade ago, 28% of high school students worked a part-time job during the school year. To investigate whether the proportion is greater today, a random sample of 80 high school students is selected. It is discovered that 37.5% of them work part-time jobs during the school year. The guidance counselor would like to know if the data provide convincing evidence that the true proportion of all high school students who work a part-time job during the school year is greater than 0.28. The guidance counselor tests the hypotheses H0: p = 0.28 versus Ha: p > 0.28, where p = the true proportion of all high school students who work a part-time job during the school year. The conditions for inference are met. The standardized test statistic is z = 1.89 and the P-value is 0.0294. What conclusion should be made using the α = 0.05 significance level?

A real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home. To do so, the agent obtained a list of 10 comparable homes just listed for sale that were currently empty. He randomly assigned 5 of the homes to be "staged,” meaning filled with nice furniture and decorated. The owners of the 5 homes all agreed to have their homes staged by professional decorators. The other 5 homes remained empty. The hypothesis is that empty homes are not as appealing to buyers as staged homes and, therefore, sell for lower prices than staged homes. The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. A dotplot of each sample shows no strong skewness and no outliers.

Lucy recently asked the servers at her restaurant to only give straws to customers who request them. She thinks that about half of the customers will ask for straws but hopes that the rate will be less than half. She randomly selects 100 customers and finds that 43 of them ask for a straw. To determine if these data provide convincing evidence that the proportion of customers who will ask for a straw is less than 50%, 150 trials of a simulation are conducted. Lucy is testing the hypotheses: H0: p = 50% and Ha: p < 50%, where p = the true proportion of customers who will ask for a straw. Based on the results of the simulation, what is the estimate of the P-value of the test?

A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. Let p = the true proportion of times the dime would land on heads when spun. Under the assumption that the true proportion is 0.5, 100 simulated proportions for samples of size 25 is shown in the dotplot. Using the dotplot, is there evidence that the proportion of times a spun dime lands on heads is greater than 0.5?

One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The distribution for X is shown in the table.Which of the following is the correct interpretation of P(X ≤ 3)?

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 with the values, 0, 1, 2, 5, and 10. Whatever space it lands on, the participant wins that value. Let X represent the value of a random spin. The distribution is given in the table.

The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. The salaries of professional football players are also heavily skewed right with a mean of $1.9 million and a standard deviation of $1.5 million. A random sample of 40 baseball players’ salaries and 35 football players’ salaries is selected. The mean salary is determined for both samples. Let represent the difference in the mean salaries for baseball and football players. Which of the following represents the standard deviation of the sampling distribution for ?

The owner of a fitness watch would like to determine if the mean number of steps he takes per day differs from the recommended 10,000 steps per day, using α = 0.01. He selects a random sample of 50 days with the intention of testing the hypotheses H0:μ = 10,000 steps versus Ha:μ ≠ 10,000 steps where μ = the true mean number of steps taken per day.Which of the following values of the alternative hypothesis would yield the greatest power to reject the null hypothesis?

A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher.Based on the 90% confidence interval, (0.02, 0.12), is there convincing evidence that the new formula of laundry detergent is better?

A shipping company claims that 95% of packages are delivered on time. A student wants to conduct a simulation to estimate the number of packages that would need to be randomly selected to find a package that was not delivered on time. The student assigns the digits to the outcomes.00-04 = package not delivered on time05-99 = package delivered on timeHere is a portion of a random number table.Beginning at line 1, and starting each new trial right after the previous trial, carry out 5 trials of this simulation. Based on the 5 trials, what is the average number of packages that need to be selected in order to find a package that was not delivered on time?

At a local college, an admissions officer surveys the incoming class of 1,000 first-year students concerning their preference of major. The officer randomly selects 100 of them and asks if they intend to major in liberal arts. Of the 100 first-year students, 62 state they intend on majoring in liberal arts. Assuming the conditions for inference have been met, what is the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts?

How many 5-letter combinations can be created from the letters in the word “friendly”? Assume that the order of the letters does not matter.