Q.6 A fuel oil company claims that one-fifth of the homes in a certain city are heated by oil. Do we have reason to believe that fewer than 1/5 are heated by oil if, in a random sample of 1000 homes in this city, it is found that 136 are heated by oil?
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- 8) A certain group of parents reports that Amino Food Supplement did not help increase the weight of their own children. The manufacturer of the food supplement then conducted a study on a random sample of children by getting their weight, giving them the food supplement for a month, and getting their weight again. Following is the sample data set on weights (in pounds) Child Without FS With FS 1 63 79 2 93 92 3 84 91 4 72 80 65 69 72 85 7 91 99 8 71 81 What is the conclusion here, at 0.01 level of significance? CO1.1 A lecturer wants to know if his statistics class has a good grasp of basic maths from matric level. Eleven students are chosen at random from the class and given a maths proficiency test. The lecturer wants the class to be able to score above 75 on the test to show that they had a good grasp of basic maths. The eleven students get scores shown below: 62 88 71 50 67 70 92 75 68 83 95 Can the lecturer be 95 percent confident that the students had a good grasp of basic maths?6
- A study of fox rabies in a country gave the following information about different regions and the occurrence of rabies in each region. A random sample of n1 = 16 locations in region I gave the following information about the number of cases of fox rabies near that location. x1: Region I Data 2 8 8 8 6 8 8 1 3 3 3 2 5 1 4 6 A second random sample of n2 = 15 locations in region II gave the following information about the number of cases of fox rabies near that location. x2: Region II Data 1 1 5 1 4 8 5 4 4 4 2 2 5 6 9 (i) Use a calculator with sample mean and sample standard deviation keys to calculate x1 and s1 in region I, and x2 and s2 in region II. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a 5% level of significance. (Assume the distribution of rabies cases in both regions is…A random sample of n1 = 16 communities in western Kansas gave the following information for people under 25 years of age. x1: Rate of hay fever per 1000 population for people under 25 97 91 122 130 94 123 112 93 125 95 125 117 97 122 127 88 A random sample of n2 = 14 regions in western Kansas gave the following information for people over 50 years old. x2: Rate of hay fever per 1000 population for people over 50 94 111 100 95 110 88 110 79 115 100 89 114 85 96 What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.)3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.
- 1.2 A lecturer wants to know if his statistics class has a good grasp of basic maths from matric level. Eleven students are chosen at random from the class and given a maths proficiency test. The lecturer wants the class to be able to score above 75 on the test to show that they had a good grasp of basic maths. The eleven students get scores shown below:62 88 71 50 67 70 92 75 68 83 95Can the lecturer be 95 percent confident that the students had a good grasp of basicmaths?The data summarized in the accompanying table is from a paper. Suppose that the data resulted from classifying each person in a random sample of 48 male students and each person in a random sample of 88 female students at a particular college according to their response to a question about whether they usually eat three meals a day or rarely eat three meals a day. Male Female Usually Eat 3 Meals a Day 25 35 Rarely Eat 3 Meals a Day 23 53 Is there evidence that the proportions falling into each of the two response categories are not the same for males and females? Use the x² statistic to test the relevant hypotheses with a significance level of 0.05. Calculate the test statistic. (Round your answer to two decimal places.) x² = Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value = What can you conclude? O Reject Ho. There is convincing evidence that the proportions falling into the two response categories are not the same for males and females. O…Every day in the summer months a supermarket receives a shipment of peaches. The supermarket’s quality inspector arranges to have one box randomly selected from each shipment for which the number of “spoiled” peaches (out of 48 peaches in the box), which cannot be put out on the supermarket shelves, is recorded. DS 6.1.5 shows the data set obtained after 55 days. Define the population from which the sample is taken. Do you think that it is a representative sample?
- 1. Six batteries taken at random from a large lot were subjected to life tests with the following results: 19, 22, 18, 16, 25, and 20 hours. Find the probability that the sample mean of x= 20 hours, as observed here, or one less than 20 hours could arise if the true mean of the lot of batteries is 21.5 hours, assuming a known variance of o = 10 hours, for the individual batteries in the lot. %3DA random sample of n1 = 16 communities in western Kansas gave the following information for people under 25 years of age. x1: Rate of hay fever per 1000 population for people under 25 100 92 122 127 93 123 112 93 125 95 125 117 97 122 127 88 A random sample of n2 = 14 regions in western Kansas gave the following information for people over 50 years old. x2: Rate of hay fever per 1000 population for people over 50 93 112 100 97 111 88 110 79 115 100 89 114 85 96 State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 ≠ ?2 H0: ?1 > ?2; H1: ?1 = ?2 H0: ?1 = ?2; H1: ?1 > ?2 H0: ?1 = ?2; H1: ?1 < ?2 What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that…p3
