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Researchers conducted a study to investigate the factors affecting the progression of pneumonia in novel coronavirus disease 2019 (COVID-19) patients who were admitted to three tertiary hospitals in Wuhan between December 30, 2019 and January 15, 2020. They collected individual data, laboratory indices, imaging characteristics, and clinical data, including albumin levels (g/L). Albumin is a protein produced by your liver that helps to keep fluid in your bloodstream, so it does not leak into other tissues. It also carries hormones, vitamins, and enzymes throughout your body. Low albumin levels can indicate a problem with your liver or kidneys. Based on clinical typing results, the patients were divided into a progression group (n=11) or an improvement/stabilization group (n=67). The mean albumin level in the progression group was 36.62 g/L with a standard deviation of 6.60 g/L. The mean albumin level in the improvement/stabilization group was 41.27 g/L with a standard deviation of 4.85 g/L. Using a 0.05 significance level, you need to test the claim that patients in the progression group had significantly lower albumin levels than patients in the improvement/stabilization group. To do so, assume the population variances are equal and answer each of the following questions.
What is the null and alternative hypothesis?
Design an algorithm to simulate chi-square distribution with 2k freedom via general transformation method.
Find the probability of a type I error α if the true proportion is p=0.6.
Can college conclude that students in new program are significantly different from rest of freshmen class? Use two - tailed test with a = 0.05.
An ordinary deck of 52 cards is well-shuffled, and then the cards are turned face up one-by-one until an ace appears. Find the expected number of cards that are
Let X1, X2, . . . , X80 be a random sample of size n = 80 from a distribution with probability density function f(x) = 6x(1 - x), 0
Uniform random numbers.- What important fact about continuous random variables does comparing your answers to parts (a) and (b) illustrate?
When asked for the probability, state the answer in the form b(n, p, x). There is no need to give the numerical value of the probability.
A gives a lower average mileage than mark B? Find the value of p, interpret the result. What assumptions should you take to work on this problem?
Carnival. A carnival game offers a $100 cash prize for anyone who can break a balloon by throwing a dart at it. It costs $5 to play, and you're willing.
What is the standard deviation of the sampling distribution?(Use 3 decimal digits)
What was 'political consensuses? How does it compare to the current political discourse in the US today?
Assume this average is based on a random sample of 25 plots and that the sample standard deviation is 100 bottles. Give a 95% confidence interval for the population average number of bottles per plot.
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