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A: Given that, A sample of n=16 scores is selected from a normal population with μ=56 and σ=20.
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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- Suppose the probability of incorrectly transmitting a single bit is . Compute the probability of correctly receiving a -word coded message made up of -bit words.Suppose the probability of erroneously transmitting a single digit is P=0.03. Compute the probability of transmitting a 4-bit code word with (a) at most one error, and (b) exactly four errors.A statistician read that 77% of the population oppose replacing $1 bills with $1 coins. To see ifthis claim is valid, he selected a sample of 80 people and found that 55 were opposed toreplacing the $1 bill. At α = 0.01, test the claim that at least 77% of the population are opposedto change
- Several researchers have found empirical evidence for a phenomenon known as the"other raceeffect" (ORE), where people are quicker and more accurate when identifying faces of their ownrace, relative to faces from other races. A single group of 35 Caucasian participants were showna series of faces (50 faces were Caucasian, 50 faces were Asian) in a learning phase. Next,participants were shown a total of 100 faces from each race, some of which were present in thelearning trials, Participants were asked to state whether or not a face was present or absent inthe learning trials. They compared the accuracy for memory of the Caucasian vs. Asian faces.If testing hypotheses about the effects of race on memory of faces, it would be most appropriateto calculate a..1)Independent- sample t-test 2)Paired sampled t-test3) One- sample t-test 4) Z-testThe experiment is to toss two balls into four boxes in such a way that each ball is equally likelyto fall in any box. Let X denote the number of balls in the first box.a. What is the CDF of X?4. A city official claims that the proportion of all commuters who are in favor of an expandedpublic transportation system is 50%. A newspaper conducts a survey to determine whetherthis proportion is different from 50%. Out of 225 randomly chosen commuters, the surveyfinds that 90 of them reply yes when asked if they support an expanded public transportationsystem. Test the official’s claim at α = 0.05.
- At pandemic time of COVID 19 surveys are conducted in two townships which fall into the same Lusaka city. In Chawama, 175 tested positive out of a sample of 318 who were tested for COVID 19. In Kabulonga, 143 tested positive out of a sample of 307 who were tested for COVID 19. At the 5% level, is there a difference between the proportions of those who tested positive in each area1. Researchers suspect that 18% of all high school students smoke at least one pack of cigarettes a day. At a high school, a randomly selected sample of 300 students found that 50 students smoked at least one pack of cigarettes a day. At ? = 0.05, test the claim that less than 18% of all high school students smoke at least one pack of cigarettes a day. Use the P-value method.n a study of red/green color blindness, 700 men and 2100 women are randomly selected and tested. Among the men, 61 have red/green color blindness. Among the women, 4 have red/green color blindness. Test the claim that men have a higher rate of red/green color blindness.(Note: Type ‘‘p_m″ for the symbol pmpm , for example p_m not=p_w for the proportions are not equal, p_m>p_w for the proportion of men with color blindness is larger, p_m<p_w, for the proportion of men is smaller. ) (a) State the null hypothesis: (b) State the alternative hypothesis: (c) The test statistic is (d) Is there sufficient evidence to support the claim that men have a higher rate of red/green color blindness than women? Use a 10 % significance level.A. YesB. No (e) Construct the 90% confidence interval for the difference between the color blindness rates of men and women. Blank <(pm−pw)< Blank
- A researcher wishes to see whether there is a difference in the weight loss ofwomen following one of the three special diets. Women are randomly assignedto the three groups and placed on the diet for 2 months. The weight losses (inpounds) are shown here. At α = 0.05, can the researcher conclude that there isa difference in diets?Of the total 161 patients with diabetes ketoacidosis (DKA), 13 had DKA before and after the pump therapy, 128 did not have DKA either before or after, 7 had DKA before but not after, and 13 did not have DKA before but after.a) Draw a 2 by 2 table b) Is there any evidence of a difference in the effect? c) Write a brief summary of what the result show.Suppose that in manufacturing a very sensitive electronic component, a company and its customers have tolerated a 2% defective rate. Recently, however, several customers have been complaining that there seem to be more defectives than in the past. Given that the company has made recent modifications to its manufacturing process, it is wondering if in fact the defective rate has increased from 2%. For quality assurance purposes, you decide to randomly select 1,000 of these electronic components before they are shipped to customers. Of the 1,000 components, you find 25 that are defective. Assume that the company produces a very large number of these components on any given day. Set up an appropriate hypothesis to test whether or not the defect rate has increased. Before proceeding to test your hypothesis, check that all assumptions and conditions are satisfied for such a test. Conduct the test using a .05 level of significance (alpha) and state your decision about…