(1-Show a frequency distribution of the final grades in mathematics & Statistics of 30 students are recorded in the accompanying table . Stat. Math. Stat. Math. Stat. Math. Stat. Math. Stat. Math. 50 55 80 75 53 50 57 90 76 71 70 72 68 72 65 73 75 93 93 81 80 62 65 85 86 90 92 64 67 61 60 83 82 56 52 74 72 94 96 82 85 63 60 86 81 91 92 77 72 79 75 84 81 60 57 75 70 78 77
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- From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 employee a employee b employee c employee d mean 21.6 14.8 15.0 22.0 s 3.4 ? 3.8 ? c) Find variance between sample,d) Find variance within sample, e) Calculate the test statistic, F.f) Determine the numerator and denominator.g) Find the critical value of F at the 5% significance level, and test the claim that the mean numberof customers served per hour by each of these four employees is…From time to time, the UTM Human Resource (UTMHR) department observes various employees fortheir work productivity. Recently UTMHR wanted to check whether the four employees at theDepartment XYZ counters, serve on average the same number of customers per hour. The HR managerobserved each of the four employees for a certain number of hours. The following Table 5 gives thenumber of customers served by the four employees during each of the observed hours. employee a employee b employee c employee d 19 14 11 24 21 16 14 19 26 14 21 21 24 13 13 26 18 17 16 20 a) Define the hypothesis null, H0 and hypothesis alternative, H1.b) Given below are means and standard deviation for some of the employees. Calculate thestandard deviation for Employee B and D.Question 4a. A large accountancy firm finds that over the long run 10% of its statements for clients are in error in some way. A quality assurance officer at the firm investigating the source of the errors takes a sample of 20 statements produced by a single employee and classifies each as being “in error” or “not in error”.i. If the variable X is used to represent the number of statements in the sample that are in error, and assuming the error rate is the firm’s level of 10% then state:• the type of distribution this variable has; and• the parameter/s of this distribution. ii. Determine the probability that 2 or less returns in this sample are in error. The quality assurance officer found that there were 5 statements in the sample that were in error.iii. Determine the probability of finding 5 or more returns in error if indeed the error rate was 10%. iv. Based upon your answer for part iii., what conclusion might the quality assurance office make about this employee in terms of the…
- Question 3 Hermie's average 5-day natural gas usage rate is 5.9Therms5days . What are her 1-day, and 8-day, natural gas usage rates? 1.18Therms1day,7.375Therms8days 0.7375Therms1day,9.44Therms8days 1.18Therms1day,9.44Therms8days 0.7375Therms1day,7.375Therms8daysResistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?CHAPTER 7 , QUESTION 2/3 Application of The Central Limit Theorem for Sums100 North Main Street is the tallest building in Winston-Salem, NC standing at 460ft tall (5520inches).Use the scenario above to determine the selected probabilities below. You may wish to use the Normal Distribution Calculator hosted by the University of Iowa's Department of Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used in class. (link: Normal Distribution Calculator) Given that the heights of American women follow the distribution N(65,3.5)N(65,3.5), what is the probability of that a random sample of 85 women, stacked head-to-foot, would be at least as tall as 100 North Main Street?P(ΣX≥5520)=P(ΣX≥5520)= (Include 5decimal places.) Determine the z-score of ΣX=5520ΣX=5520 for a sample of 85.z=z= (Include 5 decimal places.)
- Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?Human blood types are classified by three gene forms A, B, and O. Blood types AA, BB, and OO are homozygous, and blood types AB, AO, and BO are heterozygous. If p, q, and r represent the proportions of the three gene forms to the popula-tion, respectively, then the Hardy-Weinberg Law asserts that the proportion Q of heterozygous persons in any specific population is modeled by Q(p, q, r) = 2(pq + pr + qr), subject to p + q + r = 1. Find the maximum value of Q.1. A University Director wants to see whether the average time (in minutes) it takesstudents to reach classes on time is different for three groups. The data are shown here.Junior Senior Graduates35 9 1518 3 627 12 2724 6 2221 12 2414821a) At α=0.05, can the owner conclude that there is a significant difference among themeans?b) If there is a significant difference among the means, test each pair of means?
- 9. A research center claims that 24% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 28% say that they would travel into space on a commercial flight if they could afford it. At α=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. Question content area bottom Part 1 (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not enter your response here %. B. No more than enter your response here % of adults in the country would travel into space on a commercial flight if they could afford it. C. At least…A manufacturer of “Keep It Warm” bags is interested in comparing the heat retention of bags when used at five different temperatures (100°F, 125°F, 150°F, 175°F, and 200°F). Thirty bags are selected randomly from last week’s production and randomly assigned, six each, to five different groups. Items from group 1 at beginning temperature 100°F were kept in bags for an hour, and the temperatures of those items were recorded after an hour. Similarly, groups 2 to 5 were assigned items at 125°F, 150°F, 175°F, and 200°F, respectively. Identify the type of study used here. What type of inference is possible from this study?Can you provide any explanation for these results? For THE 3 TABS BELOW: Tab 1, Tab 2 & Tab 3 TAB 1. Year Age of Miss America Murder by steam, hot vapors and hot objects Dev(x) Dev(y) CP 1999 24 7 1.9 2.5 4.69 2000 24 7 1.9 2.5 4.69 2001 24 7 1.9 2.5 4.69 2002 21 3 -1.1 -1.5 1.69 2003 22 4 -0.1 -0.5 0.05 2004 21 3 -1.1 -1.5 1.69 2005 24 8 1.9 3.5 6.60 2006 22 4 -0.1 -0.5 0.05 2007 20 2 -2.1 -2.5 5.32 2008 19 3 -3.1 -1.5 4.78 2009 22 2 -0.1 -2.5 0.23 Mean 22.1 5 Sum 34.45 Standard Deviation 1.75810 2.25227 Covariance 3.45 Correlation Coefficient 0.87013 0.87013 TAB 2 Year Letter in Winning World of Scripps National Spelling Bee Number of people Killed by venomous spider Dev(x) Dev(y) CP 1999 9 6 -1.0 -1.4 1.36 2000 8 5…