Concept explainers
.43 Rock-paper-scissors: Rock-paper-scissors is a hand game played by two or more people where players choose to sign either rock, paper, or scissors with their hands. For your AP Statistics class project, you want to evaluate whether players choose between these three options randomly, or if certain options are favored above others. You ask two friends to play rock-paper-scissors and count the times each option is played. The following table summarizes the data:
Rock | Paper | Scissors |
---|---|---|
43 | 21 | 35 |
Use these data to evaluate whether players choose between these three options randomly, or if certain options are favored above others. Make sure to clearly outline each step of your analysis, and interpret your results in context of the data and the research question.
The hypotheses to test the research question are:
- Ho: people choose rock twice as much as paper
Ha: paper is the best choice - Ho: prock = .43, ppaper = .21, pscissors = .35
Ha: at least one of the probabilities is different - Ho: the distribution is uniform
Ha: this distribution is not uniform
The value of the test statistic is: Incorrect (please round to two decimal places)
The degrees of freedom associated with this test are: Correct
The p-value associated with this test is: (please round to four decimal places)
Discuss the conclusion of the test in the context of the research study:
- The data provide sufficient evidence to claim that rock, paper, and scissors are not chosen equally as often as one another
- The data do not provide sufficient evidence to claim that rock, paper, and scissors are not chosen equally as often as one another
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps with 2 images
- The operations manager of a company that manufactures tires wants to determine whether there are any differences in the quality of workmanship among the three daily shifts. She randomly selects 499 tires and carefully inspects them. Each tire is either classified as perfect, satisfactory, or defective, and the shift that produced it is also recorded. The two categorical variables of interest are: shift and condition of the tire produced. The data can be summarized by the accompanying two-way table. Perfect Satisfactory Defective Total Shift 1 106 124 2 232 Shift 2 66 85 3 154 Shift 3 36 74 3 113 Total 208 283 8 499 A) This sample has degree of freedom:��= If shift and quality are independent, thenB) With any expected count accurate to 2 decimal places, the expected count in row 1 column 1 is�1,1= C) With any component accurate to 2 decimal places, the component value in row 1 column 1 of the table iscomponent1,1= D) �2 value of this sample is�2= . Round to 2 decimal…arrow_forwardA new statistics book has been written and a faculty member and a student are asked to rank the new book and the other five best statistics books. How much do the student and professor agree on their assessment of the books (1 being the favorite, 6 being the least)? Use the data below to answer the following question:arrow_forwardThe Census Bureau Web site gives several choices for "average income" in its historical income data. In 2006, the median income of American households was $48,201. The mean household income was $66,570. The median income of families was $58,407, and the mean family income was $77,315. The Census Bureau says, “Households consist of all people who occupy a housing unit. The term ‘family’ refers to a group of two or more people related by birth, marriage, or adoption who reside together.” Identify the reason for mean incomes for households being higher than median incomes for households.arrow_forward
- review(7a): The following table summarizes the outcome of a study that researchers carried to determine if females expressed a greater fear of heights than male. How many categorical variables are summarized in the table? Men Women Expressed fear for heights 68 109 did not expressed a fear for heights 94 89arrow_forwardVirginia polled a large sample of individuals to find the percentage of students with known food allergies and the percentage of students without known food allergies. Which of the following could sufficiently display the data if only the two given categories are to be included? Select the correct answer below: bar graph pie chart either a pie chart or a bar graph neither a pie chart nor a bar grapharrow_forwardTwenty-nine college students, identified as having a positive attitude about Mitt Romney as compared to Barack Obama in the 2012 presidential election, were asked to rate how trustworthy the face of Mitt Romney appeared, as represented in their mental image of Mitt Romney’s face. Ratings were on a scale of 0 to 7, with 0 being “not at all trustworthy” and 7 being “extremely trustworthy.” Here are the 29 ratings: 2.6 3.2 3.7 3.3 3.4 3.6 3.7 3.8 3.9 4.1 4.2 4.9 5.7 4.2 3.9 3.2 4.5 5.0 5.0 4.6 4.6 3.9 3.9 5.3 2.8 2.6 3.0 3.3 3.7 a 95% confidence interval for the mean rating. Is there significant evidence at the 5% level that the mean rating is greater than 3.5 (a neutral rating)?arrow_forward
- A case-control study was conducted to examine the association between lung cancer and smoking in men. The case group contains 500 patients, who were diagnosed with lung cancer. Five hundred age-matched patients were recruited as controls. The study found that 50% of cases were regular smoking and the proportion is 20% among controls. a. Create a 2x2 table based on the given informationarrow_forwardA sample of 200 college undergraduates was collected and the student’s gender and method of getting to class that day were collected. The data appears below. Gender Drive Bike Walk Total Male 95 10 10 115 Female 65 5 15 85 Total 160 15 25 200 What proportion of the students are both female and ride a bike to class?arrow_forward(c) Draw a boxplot of the differenced data. Does this visual evidence support the results obtained in part (b)? Which boxplot below represents the data? A. O C. -6 -6 -4 -2 Differences -2 Differences 2 Q 2대 B. -6 -6 -4 -4 -2 Differences Differences 0 0 2arrow_forward
- You may need to use the appropriate technology to answer this question. Scores in the first and fourth (final) rounds for a sample of 20 golfers who competed in PGA tournaments are shown in the following table. Player FirstRound FinalRound Michael Letzig 70 72 Scott Verplank 71 72 D. A. Points 70 75 Jerry Kelly 72 71 Soren Hansen 70 69 D. J. Trahan 67 67 Bubba Watson 71 67 Reteif Goosen 68 75 Jeff Klauk 67 73 Kenny Perry 70 69 Player FirstRound FinalRound Aron Price 72 72 Charles Howell 72 70 Jason Dufner 70 73 Mike Weir 70 77 Carl Pettersson 68 70 Bo Van Pelt 68 65 Ernie Els 71 70 Cameron Beckman 70 68 Nick Watney 69 68 Tommy Armour III 67 71 Suppose you would like to determine if the mean score for the first round of a PGA Tour event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration…arrow_forwardA professor wants to know which type of instructional mode students had more satisfaction. The professor randomly selected n = 5 students from each of the following types of classes: online only, hybrid, and face-to face only. Student were given a satisfaction survey. Are their differences in student satisfaction among the different instructional modes. The data are below: Online Hybrid Face-to-Face 3 3 4 3 3 1 3 1 3 2 2 2 2 1 3 Using the table in the back of the book, find the critical value for F (Fcrit) with α = .05.arrow_forwardCan I get some help with identifying the variables and individuals?arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman