The values of the empty cells (numbered: 1,2,3,4, in red color), :respectively, are Source of Variation Between Groups Within Groups SS 321.3325 MS 2 24 8.2514 Total 519.3668 27
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A: Shown below
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A: here given minimum = 7 maximum = 70 number of classes = 6
Q: B 3 7 8 5 15 10
A: Venn diagram
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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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- A nationwide company specializing in preparing students for college and graduate school entrance exams, such as the SAT, ACT, and LSAT, had the business objective of improving its ACT preparatory course. Two factors of interest to the company are the length of the course (a condensed 10-day period or a regular 30-day period) and the type of course (traditional classroom or online distance learning). The company collected data by randomly assigning 10 clients to each of the four cells that represent a combination of length of the course and type of course. The results are organized and presented in the following table: LENGTH OF COURSE TYPE OF COURSE Condensed Regular Traditional 26 18 34 28 27 24 24 21 25 19 35 23 21…Assume that a researcher randomly selects the 15 newborn babies and counts the number of girls,d.The U.S. Census Bureau conducts annual surveys to obtain information on the percentage of the voting-age population that is registered to vote. Suppose that 642642 employed persons and 745745 unemployed persons are independently and randomly selected, and that 376376 of the employed persons and 300300 of the unemployed persons have registered to vote. Can we conclude that the percentage of employed workers ( p1p1 ), who have registered to vote, exceeds the percentage of unemployed workers ( p2p2 ), who have registered to vote? Use a significance level of α=0.1α=0.1 for the test. Step 1 of 6: State the null and alternative hypotheses for the test. Step 2 of 6: Find the values of the two sample proportions, pˆ1p^1 and pˆ2p^2. Round your answers to three decimal places. Step 3 of 6: Compute the weighted estimate of p, p‾‾p‾. Round your answer to three decimal places. Step 4 of 6: Compute the value of the test statistic. Round your answer to two decimal places. Step 5 of 6: Determine…
- A serving for brand recognition is done and it is determined that 68% of consumers have heard of dull computer company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 490 for consumers who recognize the dull computer company name?An opinion poll was conducted by the Morris Polling Group. Respondents were classified according to their sex (M or F), political affiliation (D, I, R), and the region of the country in which they reside (NW, W, C, S). Use the generalized multiplication principle to determine the number of possible classifications. A manufacturer of cereal is considering three alter native box colors—red, yellow, and blue. To check whether such a consideration has any effect on sales, 16 stores of approximately equal size are chosen. Red boxes are sent to 6 of these stores, yellow boxes to 5 others, and blue boxes to the remaining 5. After a few days a check is made on the number of sales in each store. The results (in tens of boxes) shown in the following table were obtained. Red Yellow Blue 43 52 61 52 37 29 59 38 38 76 64 53 61 74 79 81a. Calculate the within-groups, between-groups, and total sum of squares.b. Complete the analysis of variance table, and test the null hypothesis that the population mean sales levels are the same for all three box colors.
- A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below. Ethnicity Seat belt worn Hispanic Non-Hispanic Total Yes 30 149 179 No 280 333 613 Total 310 482 792 She is interested to use this table to do a test of independence with a level of significance of 0.01. What is the conclusion of this test?The accompanying data represent the gender and party affiliation of registered voters based on a random sample of 807 adults. Determine what percentage of the Republican is female based on the sample data, and select from the following choices. Republican Democrat Independent Row Totals Male 105 150 150 405 Female 120 103 179 402 Column Totals 225 253 329 807Compute for P35, P55, Q1, Q2, and Q3 based on the given data.
- A manufacturing company that produces laminate for countertops is interested in studying the relationship between the number of hours of training that an employee receives and the number of defects per countertop produced. Ten employees are randomly selected. The number of hours of training each employee has received is recorded and the number of defects on the most recent countertop produced is determined. The results are as follows. Hours of Training Defects per Countertop 1 5 4 1 7 0 3 3 2 5 2 4 5 1 5 2 1 8 6 2 Copy Data The estimated regression line and the standard error are given. Defects per Countertop=6.717822−1.004950(Hours of Training)se=1.229787se=1.229787 Suppose a new employee has had 5 hours of training. What would be the 90% prediction interval for the number of defects per countertop? Round your answer to two decimal places.uman blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor the B antigen is present, the letter O is used. The following table gives the percent of a certain country's population having each of the eight possible blood types in the sample space. Note that the presence or absence of the Rh antigen is indicated by the symbols + or −, respectively. Blood Types A+ A− B+ B− AB+ AB− O+ O− Percent 35.9 6.1 9.5 2.5 3.2 0.8 37.2 4.8 (a) What is the probability that a person selected randomly from the population has a blood type that is type O or Rh+? (b) What is the probability that a person selected randomly from the population has a blood type that contains the A antigen? (c) What is the probability that a person selected randomly from the population has a blood type that is type AB or Rh−?From a team of 27 baseball players a group of 6 is to be randomly selected for steroid testing. In how many different ways could this be done? 27P6?