chapter 11 stats 100% CORRECT SOLUTION

Ecologists conducted a study to investigate the potential ecological impact of golf courses. Investigators monitored the reproductive success of bluebirds in birdhouses at nine golf courses and ten similar birdhouses at nongolf sites. Data on nests in birdhouses occupied only by bluebirds are shown in the table. Observed Number of Nests per Birdhouse by Location 0 nests1 nest2 or 3 nestsTotalGolf3042880NongolfTotal If the proportions of nests occupied is the same for golf and nongolf sites, what would be the expected count of birdhouses with 1 nest in nongolf locations? 60 A fisheries biologist collected a random sample of fish from a lake and conducted a chi-square goodness-of-fit test to see if the distribution of fish changed over time. The table below shows the distribution of fish that were put into the lake when it was originally stocked. Fish TypeTroutBassPerchSunfishCatfishPercent25%25%20%15%15% The biologist found evidence to reject the null hypothesis in favor of the alternative hypothesis. Which of the following represents the alternative hypothesis of the test? At least one of the fish proportions is different than the corresponding proportion when the lake was originally stocked. 10 Must-Have Accessories for Sprucing Up Your Caravan A factory produces bags of rubber bands. A bag of rubber bands has five different sizes: extra large (XL), large (L), medium (M), small (S), and extra small (XS). A quality control specialist collects a random sample of 450 rubber bands from the bagging machine and calculates a chi-square goodness-of-fit test to see if the frequencies for each size in the sample match the hypothesized distribution. The quality control specialist will test his sample against the following null hypothesis Ho:pXL=0.10,pL=0.20,pM=0.40,pS=0.20,pXS=0.10Ho​:pXL​​=0.10,pL​​=0.20,pM​​=0.40,pS​​=0.20,pXS​​=0.10 How many medium rubber bands are expected in the random sample of 450 rubber bands? 180 At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the number of loans X that a randomly selected loan agent closes on a randomly selected day has the probability distribution below. x1234567P(x)0.050.100.220.300.180.120.03 At the company, the daily salary of a loan agent is $150 plus $50 per loan closed. Let Y represent the amount of money made by a randomly selected loan agent on a randomly selected day. Which of the following statements is NOT true? The mean daily salary is greater than $350 per day. A newspaper article indicated that 43 percent of cars with black seats are white, 46 percent of cars with black seats are blue, 7 percent of cars with black seats are red, and 4 percent of cars with black seats are black. A test was conducted to investigate whether the color of cars with black seats was consistent with the newspaper article. A random sample of cars of these colors was selected, and the value of the chi-square test statistic was χ2=8.2χ2=8.2. Which of the following represents the p-value for the test? P(χ2≥8.2)=0.04 Nonnative speakers of English often have characteristics in their handwriting that differ depending on the speaker's first language. Handwriting samples from a random sample of Chinese, Malay, and Indian children in a school in Singapore were taken to investigate these differences. One characteristic of interest was a rounding at the top of the capital letter A. Data for the top-rounding characteristic for a sample of 153 children are shown in the table. Observed Top Rounding on the Capital Letter A MalayIndianChineseTotalYes 921 8 38NoTotal If children from these countries exhibit top rounding in the same proportions, what is the expected count for Malay children who show top rounding? (153(38)(51)​) Let X be a random variable whose values are the number of dots that appear on the uppermost face when a fair die is rolled. The possible values of X are 1, 2, 3, 4, 5, and 6. The mean of X is 7/2 and the variance of X is 35/12. Let Y be the random variable whose value is the difference (first minus second) between the number of dots that appear on the uppermost face for the first and second rolls of a fair die that is rolled twice. What is the standard deviation of Y ? 3512​+1235​​ not just the adding one The National Park Service writes materials for students to use while in the parks. In a study of the effectiveness of some of these materials, a random sample of students was selected to take a short quiz about oak trees after using these materials. A random sample of park professionals also took the quiz. Investigators compared classifications (low, medium, and high) of the crown shapes—the general shapes of the leafy parts of the trees—made by students in s 6 through 12 with classifications made by professionals. Data from the study are shown in the table. ProfessionalsStudentsTotalLow544397Medium483987High7916Total If the professionals and the students do not differ in the distributions of their responses, which of the following is equal to the expected number of students who classify the crown shapes as medium? (200(87)(91)​) For which of the following is a chi-square goodness-of-fit test most appropriate? Determining whether a categorical variable has a significantly different distribution of proportions than the expected distribution A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27. The true population proportion of American teenagers who have a cell phone is 0.29. For samples of size 1,000 that are selected at random from this population, what are the mean and standard deviation, respectively, for the sampling distribution of the sample proportion of American teenagers who have a cell phone? 0.29,1000(0.29)(0.71)​​ the one where it's divided by 1000 Type of Grass SeedPercentFescue (F)55%Buffalo grass (B)22%Blue grama (BG)10%Indian grass (I)7%Green needlegrass (NG)6% A quality control specialist tests samples of the seed being packaged and uses a chi-square goodness-of-fit test to see whether the proportions in the samples match what is claimed by the company. Which of the following best describes the null hypothesis and the alternative hypothesis for the test? Ho:pF=0.55,pB=0.22,pBG=0.10,pI=0.07,pPNG=0.06Ho​:pF​​=0.55,pB​​=0.22,pBG​​=0.10,pI​​=0.07,pPNG​​=0.06 Ha:Ha​:At least one of the proportions is different Each person in a random sample of adults indicated his or her favorite color. The results, shown in the table below, are reported by age group of the respondents. If choice of color is independent of age group, which of the following expressions is equal to the expected number of respondents who are aged 30 to 50, inclusive, and prefer green? 314(99)(108)​ A company claims they produce their mixed bag of candies so that, of the candies in the bag, 20 percent are dark chocolate, 60 percent are milk chocolate, and 20 percent are white chocolate. In a random sample of candies of size 50, the counts are as follows: 6 dark, 32 milk, and 12 white. Assuming the conditions for inference are met, what is the test statistic for a chi-square goodness-of-fit test to investigate whether the distribution of the sample is consistent with the company's claim? χ2=10(6−10)2​+30(32−30)2​+10(12−10)2​ A local restaurant claims that it gets 45 percent of its customers from Monday through Thursday, 20 percent on Friday, 20 percent on Saturday, and 15 percent on Sunday. How many degrees of freedom should be used to conduct a chi-square goodness-of-fit test of the claim? 3 A sample of size n will be selected from a population with population proportion p. Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal? Both np and n(1 - p) are at least 10 Ms. Harper knows that her students in a computing course can choose from one of three operating systems for the semester: Doors, Banana, or Duix. Ms. Harper wants to test the hypothesis that her students will select the operating systems in the same proportion as students in other computing courses at the university. She conducts a χ2χ2 goodness-of-fit test and calculates χ2=3.79χ2=3.79with a corresponding p-value of 0.15. Which of the following is correct at a 5-percent level of significance? Fail to reject the null hypothesis, since 0.15 0.05. A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y? $432.00 The following question(s) refer to the following information.Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. If the customer rolls the dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer would expect to pay for these second movies? $9.40 A spinner made for a game of chance has 8 equally likely spaces. Alfonso records the result of a sample of 400 spins. Alfonso decides to calculate a chi-square test statistic for a goodness-of-fit test to see whether the spinner is fair. Which of the following is the appropriate null hypothesis? Ho​:p1​​=0.125,p2​​=0.125,p3​​=0.125,p4​​=0.125,p5​​=0.125,p6​​=0.125,p7​​=0.125,p8​​=0.125 regular equal sign Which of the following is not a condition for a chi-square goodness-of-fit test? The distribution of the sample should be approximately normal. Let X represent the number on the face that lands up when a fair six-sided number cube is tossed. The expected value of X is 3.5, and the standard deviation of X is approximately 1.708. Two fair six-sided number cubes will be tossed, and the numbers appearing on the faces that land up will be added. Which of the following values is closest to the standard deviation of the resulting sum? 2.415 Which of the following chi-square distributions has the smallest number of degrees of freedom? hump all the way to the left An administrator at a local high school wanted to investigate whether there is an association between the amount of time a student studies for a test and the type of extracurricular activity the student is involved in. Three hundred students selected at random were asked how long they had studied for the last math test and how many extracurricular activities they are involved in. The times they had studied were recorded as either not at all, less than 30 minutes, or more than 30 minutes. Each student also identified which extracurricular activity (out of a total of 5 extra curricular activities) they were involved in. The calculated chi-square test statistic was 7.53 with a corresponding p-value of 0.4807. Based on this p-value, which of the following is the correct decision for the appropriate hypothesis test at the α=0.05α=0.05 significance level? Fail to reject the null hypothesis. The test is not statistically significant because a p-value of 0.4807 is greater than a significance level of 0.05. For which of the following is a chi-square goodness-of-fit test most appropriate? CONTINUED.......