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An electronic implant that stimulates the auditory nerve has been used to restore partial hearing to a number of deaf people. In a study of implant acceptability (Los Angeles Times, January 29, 1985). 250 adults born deaf and 250 adults who went deaf after learning to speak were followed for a period of time after receiving an implant. Of those deaf from birth, 75 had removed the implant, whereas only 25 of those who went deaf after learning to speak had done so. Does this suggest that the true proportion who remove the implants differs for those who were born deaf and those who went deaf after learning to speak? Test the relevant hypotheses using a .01 significance level.Samples of both surface soil and subsoil were taken from eight randomly selected agricultural locations in a particular county. The soil samples were analyzed to determine both surface pH and subsoil p, with the results shown in the accompanying table. 5 7 A Surface pll 6.55 598 5.59 617 592 618 643 5.68 Subsoil pH 6.78 6.14 a. Compute a 90% confidence interval for the mean difference between surface and subsoil pH for agricultural land in this county. b. What assumptions are necessary for the interval in Part (a) to be valid?A particular cell phone case is available in a choice of four different, colors. A store sells all four colors. To test the hypothesis that sales are equally divided among the four colors, a random sample of 100 purchases is identified. a. If the resulting X2 value were 6.4, what conclusion would you reach when using a test with significance level 0.05? b. What conclusion would be appropriate at significance level 0.01 if X2 = 15.3? c. If there were six different covers rather than just four, what would you conclude if X2 = 13.7 and a test with o = 0.05 was used?The article "In Bronx, Hitting Home Runs Is A Breeze" (USA Today, June 2, 2009) included a classification of 87 home runs hit at the new Yankee Stadium according to direction that the ball was hit, resulting in the accompanying data. ConNT Right Right Field Center Center Field Number of 10 7 Home Runs 3. Assuming that it is reasonable to regard this sample of 87 home runs as representative of home runs hit at Yankee Stadium, carry out a hypothesis test to determine if there is convincing evidence that the proportion of home runs hit is not the same for all five directions. b. Write a few sentences describing how the observed counts for the five directions differ from what would have been expected if the proportion of home runs is the same for all five directions.How would you answer the following question: Next Wednesday's meeting has been moved forward two days. What day is the meeting now that it has been rescheduled? This question is ambiguous as "moved forward" can be interpreted in two different ways. Did you answer Monday or Friday? The authors of the paper "Even Abstract Motion Influences the Understanding ofTime" (Metaphor and Symbol [2011]: 260-271) wondered if the answers Monday and Friday would be provided an equal proportion of the time. A sample of students at Stanford University were asked this question, and the responses are summarized in the following table. Response |Frequency Monday 11 Friday 33 The authors of the paper used a chi-squared goodness-of-fit test to test the null hypothesis HO : p1 = 0.50, p2 = 0.50, where p1 is the proportion who would respond Monday and p2 is the proportion who would respond Friday. They reported X2 = 11.00 and P-value:0.001. What conclusion can be drawn from this test?An article about the California lottery that appeared in the San Luis Obispo Tribune (December 15, 1990) gave the following information on the age distribution of adults in California: 35% are between 18 and 34 years old, 51% are between 35 and $4 years old, and 14%% are 85 years old or older. The article also gave information on the age distribution of those who purchase lottery tickets. The following table is consistent with the values given in the article: Age of Purchaser Frequency 18-34 36 35-64 130 65 and over 34 Suppose that the data resulted from a random sample of 200 lottery ticket purchasers. Based on these sample data, is it reasonable to conclude that one or more of these three age groups buys a disproportionate share of lottery tickets? Use a chi-square goodness-of-fit test with o= .05.A certain genetic characteristic of a particular plant can appear in one of three forms (phenotypes). A researcher has developed a theory, according to which the hypothesized proportions are p. = .25, p, = .50, and p, = .25. A random sample of 200 plants yields X = 4.63. 3. Carry out a test of the null hypothesis that the theory is correct, using level of significancea=.05. b. Suppose that a random sample of 300 plants had resulted in the same value of X". How would your analysis and conclusion differ from those in Part (a)?The article "Linkage Studies of the Tomato" (Transactions of the Royal Canadian Institute [1931]: 1-19) reported the accompanying data on phenotypes resulting from crossing tall cut-leaf tomatoes with dwarf potato-leaf tomatoes. There are four possible phenotypes: (1) tall cut-leaf, (2) tall potato-leaf, (3) dwarf cutleaf, and (4) dwarf potato-leaf. Phenotype 2 3 4 Frequency 926 288 293 104 Mendel's laws of inheritance imply that p, = 9/18, p, = 3/16, p, = 3/16, and p, = 1/18. Are the data from this experiment consistent with Mendel's laws? Use a _01 significance levelA particular state university system has six campuses. On each campus, a random sample of students will be selected, and each student will be categorized with respect to political philosophy as liberal, moderate, or conservative. The null hypothesis of interest is that the proportion of students falling in these three categories is the same at all six campuses. a. On how many degrees of freedom will the resulting X"test be based? b. How does your answer in Part (a) change if there are seven campuses rather than six? C. How does your answer in Part (3) change if there are four rather than three categories for political philosophy?A random sample of 1000 registered voters in a certain county is selected, and each voter is categorized with respect to both educational level (four categories) and preferred candidate in an upcoming election for county supervisor (five possibilities). The hypothesis of interest is that educational level and preferred candidate are independent. a. If X" = 7.2. what would you conclude at significance level .10? b. If there were only four candidates running for election, what would you conclude if X* = 14.5 and a = .05?The paper "Contemporary College Students and Body Piercing" (Journal of Adolescent Health [2004]: 58-61) described a survey of 450 undergraduate students at a state university in the southwestern region of the United States. Each student in the sample was classified according to class standing (freshman, sophomore, junior, or senior) and body art category (body piercings only, tattoos only. both tattoos and body piercings, no body art). Use the data in the accompanying table to determine if there is evidence that there is an association between class standing and response to the body art question. Assume that it is reasonable to regard the sample of students as representative of the students at this university. Use o= _01. Body Both Body Piercings Tauloos Piercing and No Body Only Only Art Freshman 61 14 BG Sophomore 11 Junior 43 Senior 21 17 54The accompanying data on degree of spirituality for a sample of natural scientists and a sample of social scientists working at research universities appeared in the paper "Conflict Between Religion and Science among Academic Scientists" (Journal for the Scientific Study of Religion [2000]: 276-282). Assume that it is reasonable to regard these two samples as representative of natural and social scientists at research universities. Is there evidence that the spirituality category proportions are not the same for natural and social scientists? Test the relevant hypotheses using a significance level of .01. Degree of Spirituality Very Moderate Slightly Not OC All Natural Scientists 162 TOR 211 Sodal Sciences 223 213 259The authors of the paper "Movie Character Smoking and Adolescent Smoking: Who Matters More, Good Guys or Bad Guys?" (Pediatrics [2009]: 135-141) classified characters who were depicted smoking in movies released between 2000 and 2005. The smoking characters were classified according to sex and whether the character type was positive, negative or neutral. The resulting data is given in the accompanying table. Assume that it is reasonable to consider this sample of smoking movie characters as representative of smoking movie characters. Do the data provide evidence of an association between sex and character type for movie characters who smoke? Use 0= .05. Characer Type SEN Negathe Neutral Male 255 106 130 Female 12\fDoes including a gift with a request for a donation affect the proportion who will make a donation? This question was investigated in a study described in the report "Gift-Exchange in the Field" (Institute for the Study of Labor, 2007). In this study, letters were sent to a large number of potential donors in Germany. The letter requested a donation for funding schools in Bangladesh. Those who were to receive the letter were assigned at random to one of three groups. Those in the first group received the letter with no gift. Those in the second group received a letter that included a small gift (a postcard), and those in the third group received a letter with a larger gift (four postcards). The response of interest was whether or not a letter resulted in a donation. No Donation No Gift Small Gift 2772 Large Cilic 3. Carry out a hypothesis test to determine if there is convincing evidence that the proportions in the two donation categories are not the same for all three types of requests. Use a significance level of .01. b. Based on your analysis in Part (3) and a comparison of observed and expected cell counts, write a brief description of how the proportion making a donation varies for the three types of request.
