Consider a nano ring consists of total 12 atoms as shown below. A black atom is initially placed at the outer rim of the ring as shown in the figure below. The black atom can randomly jump (with equal probability) from atom to atom along the outer side of the ring on either side as shown by the arrows. When the black atom passes by the grey atom, it emits a pulse of light with intensity I.. Compute the total average intensity of light emitted by the black atom in 15 jumps.
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- Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correctsymbol (µ, p, Η) for the indicated parameter. An entomologist writes an article in a scientific journalwhich claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to agenetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.a) Given P (X) = 0.4, P (Y) = 0.4 and P (X/Y') = 0.25. i) Find the probability that the event Y does not occur. ii) Draw a contingency table to represent the events above. iii) Find P (XU Y).1) Malaria is a disease that destroys red blood cells (the parasite invades red blood cells, multiplies, and then infects more red blood cells). In a recent study (Kotepul, et al., 2015) looking at various blood counts, the authors found the following results. Results are in billion red blood cells / cubic mm. Note that I have deliberately modified these results (do not use R): n ̄y s Low infection 527 4.16 2.23 High infection 157 4.51 2.34 Is there a difference in red blood cell count?(Hint: please think about this before you just start working on the problem!)
- A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that they would travel into space on a commercial flight if they could afford it. At a =0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state Ho and H. 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.) O A. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not %. O B. No more than % of adults the country would travel into space on a commercial flight if they could afford it. O C. % of adults in the country would travel into space on a commercial flight if they could afford it. O D. At least % of adults in the country would travel…What is the answerA research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At a=0.01, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state Ho and H. 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.) ontents O A. No more than % of adults in the country would travel into space on a commercial flight if they could afford it. %. O B. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not edia Library O C. At least % of adults in the country would travel into space on a commercial flight if they could afford it. lan O D. % of adults…
- A company that manufactures medical devices is conducting tests in R&D on a new product. The product is in production on a pilot run (product will not be sold from the pilot run). The product is manufactured in batches and the quality of the batch must be determined, by testing a sample of 9 devices selected at random from a batch. One aspect that is monitored is the width of the bond in the device, ideally this should be equal to 3 mm on average. A sample from the latest batch gave the following bond widths measured in mm: 3.2, 2.8, 2.7, 3.0, 2.9, 2.9, 2.9, 3.2, 2.8 these gave an average of 2.93 mm and the widths varied by a standard deviation of s = 0.17 mm. Test, at significance level α = 0.01, whether there is evidence that the average bond width of the batch of devices is different to the required specification, by testing the following hypotheses: H 0: μ = 3 mm H a: μ ≠ 3 mm. Complete the test by filling in the blanks in the following:An estimate of the population mean is…A research center claims that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At a = 0.10, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H, and H 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.) O A. At least % of adults in the country would travel into space on a commercial flight if they could afford it. O B. % of adults in the country would travel into space on a commercial flight if they could afford it. %. O C. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not O D. No more than % of adults in the country would…A research center claims that 28% 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, 32% say that they would travel into space on a commercial flight if they could afford it. At a = 0.01, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state Ho 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. At least % of adults in the country would travel into space on a commercial flight if they could afford it. B. No more than % of adults in the country would travel into space on a commercial flight if they.could afford it. C. 28 % of adults in the country would travel into space on a commercial flight if they could afford it. O D. The percentage adults in the country who would travel into…
- The contingency table shows a random sample of urban, suburban, and rural libraries and the speed of their Internet access. In the table, mbps represents megabits per second. At α = 0.01 can you conclude that the metropolitan status of libraries and Internet access speed are related? Metropolitan status Access speed Urban Suburban Rural 1.4 mbps or less 5 20 58 1.5 mbps – 3.0 mbps 24 46 65 Greater than 3.0 mbps 37 59 64 What is the Chi-square test statistics and the decision for this question. The Test statistics is . Leave your answer in 3 decimal places. DECISION: We the null hypothesis.A large discount department store chain advertises on television (X₁), and on the radio (X₂). A sample of 12 of its stores in the certain area showed expenditures and revenues during a given month. All figures are in thousands of dollars. The dataset is summarised below. Television advertising X'X = X'Y = a) b) c) d) e) 12 115 1191 647 6393 Radio advertising Television & Radio advertising X'X = X'Y = 12 68 410 647 3868 0.109897957 (X'X) = -0.001810563 0.000189003 -0.001625893 -0.00000012663 0.000287136 Y'Y=39973 and b₁ = -10.11045936] 1.956197151 and Σ.Χ.Χ, = 654 7.990629999 Interpret the given slopes. Use the given information to find X'Y for the two independent variables (i.e. Television & Radio advertising). (1) Regardless of the results of the overall regression significance test, test for the significance of the individual predictors using the partial F-test. Based on your findings from c) what is your final model? Based on your final model from d) what will be the matrix of X?We are throwing darts at a disk (i.e. a filled in circle) shaped board of radius 5. We assume that the position of the dart is a uniformly chosen point in the disk. The board has a disk shaped bullseye with radius 1. Suppose that we throw a dart 1500 times at the board. Estimate the probability that we hit the bullseye at least 71 times.