STEVENS INSTITUTE OF TECHNOLOGY 1870 HOMEWORK 8 MA 541-B - Spring 2024 Show ALL WORK to get full credit. (Write the pledge on top of your work and sign under it.) Note: In your submission, you must do the following: Please manually solve all the questions and show the "Calculations" that you are doing, please don't just write the formula and the final value. Also, calculations should be very precise to get the full points. If you are just writing the formula and directly the final value, it will lead to points deduction. • Round all test statistics to four decimal places. Problem 1: Adult-onset diabetes is known to be highly genetically determined. A study was done comparing frequencies of a particular allele in a sample of such diabetics and a sample of nondiabetics. The data are shown in the following table: Bb or bb BB Diabetic 12 39 Normal 4 49 a) Are the relative frequencies of the alleles significantly different in the two groups? Use α = 0.01. b) What is the relevant odds ratio? Problem 2: Phillips and Smith(1990) conducted a study to investigate whether people could briefly postpone their deaths until after the occurrence of a significant occasion. The senior woman of the household plays a central ceremonial role in the Chinese Harvest Moon Festival. Phillips and Smith compared the mortality patterns of old Jewish women and old Chinese women who died of natural causes for the weeks immediately preceding and following the festival, using records from California for the years 1960-1984. Compare the mortality patterns shown in the table. (Week -1 is the week preceding the festival, week 1 is the week following, etc.) Use α = 0.05. Week Chinese Jewish -2 55 141 -1 33 145 1 70 139 2 49 161 Problem 3: Overfield and Klauber (1980) published the following data on the incidence of tuberculosis in relation to blood groups in a sample of Eskimos. Is there any association of the disease and blood group within the ABO system? Use α = 0.005. ABO system Severity Moderate-Advanced О A B AB 7 5 3 13 Minimal Not Present 27 32 8 18 55 50 7 24 Problem 4: Records of 317 patients at least 48 years old who were diagnosed as having endometrial carcinoma were obtained from two hospitals (Smith et al. 1975). Matched controls for each case were obtained from the two institutions; the con- trols had cervical cancer, ovarian cancer, or carcinoma of the vulva. Each control was matched by age at diagnosis (within four years) and year of diagnosis (within two years) to a corresponding case of endometrial carcinoma. This sort of design, called a retrospective case-control study, is frequently used in medical inves- tigations where a randomized experiment is not possible. The following table gives the numbers of cases and controls who had taken estrogen for at least 6 mo prior to the diagnosis of cancer. Is there a significant relationship between estrogen use and endometrial cancer? Do you see any possible weak points in a retrospective case-control design? Use a = 0.005. Controls Estrogen Used Not Used Cases Estrogen Used Not Used 39 113 15 150 Problem 5: Suppose that a company wishes to examine the relationship of gender to job sat- isfaction, grouping job satisfaction into four categories: very satisfied, somewhat satisfied, somewhat dissatisfied, and very dissatisfied. The company plans to ask the opinions of 100 employees. Should you, the company's statistician, carry out a chi- square test of independence or a test of homogeneity?

In order to target a specific region of genomic DNA with CRISPR, researchers must include a guide RNA containing a 20-basepair (bp) long spacer sequence that matches the DNA sequence at the target site. One of the possible risks of genetic engineering methods is "off-target" editing, which occurs when a guide RNA matches a part of the genome other than the intended target site. (i) How many possible guide RNA sequences are there? (ii) Estimate probability that a single site in the human genome matches a random 20-bp spacer. State all your assumptions. (iii) After infection, HIV converts its RNA genome into DNA and inserts itself into the human genome. Imagine you have designed a 20-bp spacer to target and deactivate part of the HIV DNA sequence. Based on the previous answer, estimate the probability that this sequence will have at least one off-target match somewhere in the human X chromosome, which is 300 000 bp long (counting both strands). Note: when P is very small (close to 0), (1-P)^n is approximately equal to (1-nP). (iv) What would be the probability of an off-target site appearing somewhere in the entire human genome (6 billion pairs counting both strands)?

Part 1: When reading a journal or newspaper article that cites statistics or presents statistical results, what are some things that you should consider to assess whether the conclusions are credible? Why? (Hint: review Chapter 1 and the other chapters we have covered in the textbook for specific criteria. The more criteria listed the better.)

a). Choose a specific ecosystem (eg a coral reef, a desert, a rainforest) and briefly describe a situation where human intervention has significantly altered it (either for the better or the worse). Remember to describe the ecosystem both before and after the changes and explain the factors that have caused the transformation (examples would include logging companies clearing large areas of forest or the introduction of a treatment plant that reduced the amount of raw sewage piped into the sea).

The Biologist's Experiment A biologist is investigating the effect of potential plant hormones by treating 20 stem segments. At the end of the observation period the following length averages were computed: Compound X = 1.18 Compound Y - 1.17 Based on these mean values it was concluded that there are no treatment differences. 1) Are you satisfied with this conclusion? Why or why not? 2) If you were asked for help in analyzing these data, what statistical method would you suggest to be used to come to a meaningful conclusion about the data and why? 3) Are there any other questions you would ask regarding this experiment, data collection, and analysis methods?

Q10. Section 3-2: Systolic Blood Pressure: [6 marks] the systolic blood pressure of 30 randomly selected college students is Use grouped formulas to find approximations for mean, standard deviation, median, P30 and Q3. [1] Xg= [2] Sg5 [1] grouped median [1] P30 [1] Q3 =

b). Discuss how far you believe human beings should go to protect current ecological systems (if at all) and whether you think there is ever a time when natural ecology should be sacrificed for human needs.

Part 4: After you have conducted the analysis in Part 3, the association between exposure to noise and hearing loss weakened and became statistically insignificant. Explain this finding.

Part 3: You were requested to again investigate the association between exposure to noise and hearing loss while also accounting for each worker's age, level of education, past history of a hearing ailment, and presence of comorbidity. What statistical analysis would provide an answer?

Assume that we want to construct a confidence interval. Do one of the following, as appropriate. (a) Find the critical value Za/2. (b) find the critical value ta/2, or (c) state that neither the normal nor the t distribution applies. Confidence level is 95%, o = 26.6, and the histogram of right-eye vision measurements from a random sample of 66 adult males is shown to the right. Frequency 40 30- 20 10 of 0 50 100 150 200 Vision in Right Eye Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. Za/2 (Round to two decimal places as needed.) OB. ta/2 (Round to two decimal places as needed.) OC. Neither the normal nor the t distribution applies. Next Q

QUESTION 8 price/pound US dollars 3 2 A I apples plums oranges w N price/pound US dollars B apples 10 points Save Answer plums oranges isuers/nQuestion Completion Status: pric pric AQ ✩ apples plums oranges apples plums oranges Explain how these bars and whiskers contribute to understanding of the significance of the results obtained: 100 words or less! For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph V Arial V 10pt *** O WORDS POWERED BY TINY Sign in