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- Suppose that asthma affects 1 in every 20 children in a population. You take an SRS of 250 children from this population. Can we use the Normal approximation to the binomial in this instance? What is the probability of seeing at least 25 cases in a sample?AP2.23 There are four major blood types in humans: O, A, B, and AB. In a study conducted using blood specimens from the Blood Bank of Hawaii, indi- viduals were classified according to blood type and ethnic group. The ethnic groups were Hawaiian, Hawaiian-White, Hawaiian-Chinese, and White. Suppose that a blood bank specimen is selected at random. Ethnic Group Blood Hawaiian- Hawaiian- type Hawaiians White Chinese White Total 1903 4469 2206 53,759 62,337 A 2490 4671 2368 50,008 59,537 В 178 606 568 16,252 17,604 АВ 99 236 243 5001 5579 Total 4670 9982 5385 125,020 145,057 (a) Find the probability that the specimen contains type O blood or comes from the Hawaiian-Chinese ethnic group. Show your work. (b) What is the probability that the specimen contains type AB blood, given that it comes from the Hawai- ian ethnic group? Show your work. (c) Are the events "type B blood" and "Hawaiian ethnic group" independent? Give appropriate statistical evidence to support your answer. (d) Now…In snapdragons, variation in flower color is determined by a single gene (Hartl and Jones 2005). RR individuals are red, Rr (heterozygous) individuals are pink, and rr individuals are white. In a cross between heterozygous individuals, the expected ratio of red-flowered:pink-flowered:white-flowered offspring is 1:2:1. a. The results of such a cross were 10 red-, 21 pink-, and 9 white-flowered offspring. Do these results differ significantly (at a 5% level) from the expected frequencies? b. In another, larger experiment, you count 100 times as many flowers as in the experiment in part (a) and get 1000 red, 2100 pink, and 900 white. Do these results differ significantly from the expected 1:2:1 ratio? c. Do the proportions observed in the two experiments [i.e., in parts (a) and (b)] differ? Did the results of the two hypothesis tests differ? Why or why not?
- We have seen that nonindependence of alleles (possibly caused by differential mortality of genotypes) can lead to deviations from normal proportions of offspring genotypes. Find the probability that a surviving offspring from a selfing heterozygote with genotype Aa has zero, one, or two A alleles. Which cases follow a binomial distribution? Suppose that all of the homozygous offspring survive and half of the heterozygous offspring survive.Consider a Bernoulli Experiment with 7 trials. If the expected number of “successful” trials is 4, what is the probability of a “successful trial”? What is the variance of the Binomial Distribution formed ?If a hypothesis is tested at the a=0.05 level of significance, what is the probability of making a type 1 error?
- Don't know how to solveA sample of n=64 observation (independently drawn) is selected from a population with mean 20 and s.d.16. What is the probability that the sample mean is less than 15.5?A news article estimated that only 6% of those ages 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans ages 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.06. (a) A random sample of n = 100 people will be selected from this population and p̂, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p̂? (Round your standard deviation to four decimal places.) meanstandard deviation (b) Is the sampling distribution of p̂ approximately normal for random samples of size n = 100? Explain. (Select all that apply.) the sampling distribution of p̂ is approximately normalthe sampling distribution of p̂ is not approximately normalnp is…
- Physicians at a clinic gave what they thought were drugs to 960960 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 5252 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.490.49. For the hypotheses that the proportion of improving is 0.490.49 against that it is >0.49>0.49, find the p-value. p=p=A large clinical trial of the effect of diet on breast cancer assigned women at random to either a normal diet or a low-fat diet. To check that the random assignment did produce comparable groups, we can compare the two groups at the start of the study. Asked if there is a family history of breast cancer: 1276 of the 5964 women in the low-fat group and 1507 of the 7726 women in the control group said "Yes." If the random assignment worked well, there should not be a significant difference in the proportions with a family history of breast cancer. How significant is the observed difference? State: Is there evidence of a difference in the proportion of women with a family history of breast cancer between the treatment and control groups? Plan: Let pi be the proportion for the treatment group, and Pz the proportion for the control group. State the hypotheses for your test. Ha:Pi + P2 Solve: Give the value of the test statistic. Use the calculator. Select an answer ♥ Ho:pi = p2 What is the…question 4 Diagnostic tests of medical conditions can have several types of results. The test resultcan be positive or negative, whether or not a patient has the condition. A positive test (+)indicates that the patient has the condition. A negative test (-) indicates that the patientdoes not have the condition. Remember, a positive test does not prove that the patient hasthe condition. Additional medical work may be required. Consider a random sample of200 patients, some of whom have a medical condition, and some of whom do not. Resultsof a new diagnostic test for the condition are shown. Condition ispresent Condition is absent total Test result (+) 110 20 130 Test result (-) 20 50 70 total 130 70 200 Assume the sample is representative of the entire population. For a person selected at random,compute the following probabilities:a. P(+│condition is present); this is known as the sensitivity of a test. b. P(- │condition is absent); this is known as the…