a) Based on Table 1, find a recurrence relation for the number of bit sequences of length n with an odd number of 1s? b) Show that a, = 2" is a solution of the recurrence relation you obtained in (a).
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- Engineering company has a task of checking compressive strength for 100 concrete cubes. The results revealed that 85 cubes passed the compressive strength test successfully and 15 cubes failed in the test. If 10 cubes are selected at random to be inspected by the company, determine the probability that the 8 cubes will pass the test and 2 cubes will fail in the test by using the Combinatorial Analysis. *Women executives A company is criticized because only13 of 43 people in executive-level positions are women.The company explains that although this proportion islower than it might wish, it’s not surprising given thatonly 40% of all its employees are women. What do you think? Test an appropriate hypothesis and state your con-clusion. Be sure the appropriate assumptions and condi-tions are satisfied before you proceed.In a Right Tailed Hypothesis test, the test statistic was found to be Z=2.74The rejection region included values greater than the critical value Zc=2.02 The conclusion would be to... Reject the null hypothesis because the test statistic is NOT in the rejection region Fail to reject the null hypothesis because the test statistic is in the rejection region Fail to reject the null hypothesis because the test statistic is NOT in the rejection region Reject the null hypothesis because the test statistic is in the rejection region Accept the null hypothesis because the test statistic is NOT in the rejection region
- A neuroscientist is interested in testing the effects of environment on dendritic branching in the hippocampus (dendrites increase the receptivity of neurons and may be an important basis of cognition). To test this, he took one group of rats (n = 11) and housed them in an “enriched” environment (consisting of a large box with tunnels to run through, toys to play with, etc.) and then he took another group of rats (n = 11) and housed them in an “isolate” environment (rats were housed alone without any tunnels or toys). After 6 weeks, the number of dendritic spines in a particular region of the hippocampus from these rats was imaged and counted. The results are below. Did the different housing conditions have an effect on the number of dendrite branches? Solve using the steps in hypothesis testing. Enriched condition Isolate condition Mean number of dendrites 40 10 (Estimated) Standard Deviation 10 4 Question: Calculate the upper 95% confidence interval…A neuroscientist is interested in testing the effects of environment on dendritic branching in the hippocampus (dendrites increase the receptivity of neurons and may be an important basis of cognition). To test this, he took one group of rats (n = 11) and housed them in an “enriched” environment (consisting of a large box with tunnels to run through, toys to play with, etc.) and then he took another group of rats (n = 11) and housed them in an “isolate” environment (rats were housed alone without any tunnels or toys). After 6 weeks, the number of dendritic spines in a particular region of the hippocampus from these rats was imaged and counted. The results are below. Did the different housing conditions have an effect on the number of dendrite branches? Solve using the steps in hypothesis testing. Enriched condition Isolate condition Mean number of dendrites 40 10 (Estimated) Standard Deviation 10 4 Question: Calculate the T statistic"Statistically Z-Test can be used if the sample is large ( n > 30 ) even population SD is not given". Justify this statement either by proving algebraically or computation.
- A manufacturer produces boxes of candy, each containing 10 pieces. Two machines are used for this purpose. After a large batch has been produced, it is discovered that one of the machines, which produces 40% of the total output, has a fault that has led to the introduction of an impurity into 10% of the pieces of candy it makes. The other machine produced no defective pieces. From a single box of candy, one piece is selected at random and tested. If that piece contains no impurity, what is the probability that the faulty machine produced the box from which it came?In a clinical study, a random sample of 540 participants agree to have their blood drawn, which is to be examined for the presence of antibodies against a certain contagious disease. It is found in 22% of the blood samples, which experimenters hope to extrapolate to the general population. From this random sample, 10 participants' blood samples are selected at random. If X is the number of samples out of the 10 who have these antibodies, what can we say about X? A. The sample size is not large enough for us to approximate X using a normal distribution B.The expected value of X is 22 C. X can be approximated using a normal distribution in lieu of a binomial distribution D. X has a sampling distribution that is normal3.Luijckx et al (2012) discovered that resistance to the bacterial parasite Pasteuria ramose is genetically variable in the common freshwater crustacean, Daphnia magna. To investigate the genetic basis of this variation, they crossed a completely resistant lineage to a completely susceptible lineage. All the F1 offspring were resistant. These offspring, when mature, were then crossed to each other to produce an F2 generation. If resistance is the result of only a single gene with two forms (alleles) then resistant and susceptible F offspring should occur in a 3:1 ratio. Of 71 F2’s tested, 57 were resistant and 14 were susceptible. a.With these data, calculate the range of most plausible-values for the proportion of resistant offspring. Does the plausible range include the proportion predicted if resistance is determined by a single gene? b.Give two other values for proportion that are also consistent with the data. c.Test the genetic hypothesis. Are the results compatible with the…
- We are studying the factors that contribute to unemployment at an individual level. UE, unemployment, is our dependent variable and it is a binary variable that takes the value 1 if an individual is unemployed and 0 if they are employed. We have a random sample and we estimate the following model: UE^ = 0.508 − 0.051educ − 0.023urban + 0.005age (0.122) (0.012) (0.005) (0.002) n = 6214, R2 = 0.474 where educ = an individual’s years of education urban = a dummy equal to 1 if the individual lives in an urban area and 0 otherwise age = an individual’s age in years What is the correct interpretation of the estimated coefficient on education? a) For each additional year of education, the probability of being unemployed is expected to decrease by 5.1 percentage points. b) For each additional year of education, unemployment is expected to decrease by 5.1 percent, all else equal. c) For each additional year of education, the unemployment rate is expected to…An investigator is interested in the effects of sleep deprivation on memory function. He randomly assigns each of 20 participants to one of four groups. Five subjects take a test of memory function after they have been awake for eight hours (No sleep deprivation). Five subjects take the test after they have been awake for 18 hours (mild sleep deprivation). Five subjects take the test after they have been awake four 24 hours (moderate sleep deprivation). Five subjects take the test after they have been awakefor 48 hours (severe sleep deprivation). Apply appropriate test to verify the effect of sleep deprivation on memory function.To inspect the quality of the screens for mobile phones produced by Company X, two separate inspection devices are used to test the screens for defects. Basically, a specific screen is tested once using the two inspection devices. Device 1 can detect the presence of defects 99.3% of the time, whereas Device 2 can detect defects 99.7% of the time. Assume that the 2 devices are operating independently from each other. One day, four defective screens were sent for inspection. Let X represent the number of screens that will be correctly tagged as defective by Device 1, while Y represents the number of screens that will be correctly tagged as defective by Device 2. Are X and Y independent? explain