You are given: (i) Losses follow an exponential distribution with mean 0. (ii) A random sample of losses is distributed as follows: Loss Range Number of Losses (0 – 100] 32 (100 – 200] 21 (200 – 400] 27 (400 – 750] 16 (750 – 1000] (1000 – 1500] 2 Total 100 Estimate 0 by matching at the 80th percentile. (A) 249 (B) 253 (C) 257 (D) 260 (E) 263
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- Weekly rates of return (on an annualized basis) for certain securities over a given period are believed to be normally distributed with a mean of 8.00% and variance of 0.25. Give two values x, and x, such that you are 95% sure that annualized weekly returns will be between the two values.15. For several years researchers have noticed that thereappears to be a regular, year-by-year increase in theaverage IQ for the general population. Thisphenomenon is called the Flynn effect after theresearcher who first reported it (Flynn, 1984, 1999),and it means that psychologists must continuouslyupdate IQ tests to keep the population mean at 100. To evaluate the size of the effect, aresearcher obtained a 10-year-old IQ test that wasstandardized to produce a mean IQ of 100 for thepopulation 10 years ago. The test was then given to asample of n 64 of today’s 20-year-old adults. Theaverage score for the sample was M 107 with astandard deviation of s 12.a. Based on the sample, is the average IQ for today’spopulation significantly different from the average10 years ago, when the test would have producesa mean of 100? Use a two-tailed test with.01.b. Make an 80% confidence interval estimate oftoday’s population mean IQ for the 10-year-old test.True or False? 1/n∑(Xi − X)^2 is an asymptotically unbiased estimator for the variance of X.
- A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 22 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 24 subjects were assigned to the control group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data is: nn x¯x¯ ss Treatment group (new drug) 22 23.48 8.01 Control group (old drug) 24 18.52 7.15 Without using software, how would you estimate the number of degrees of freedom for this problem? Select one: use the larger value, 23, chosen from the two options 21 and 23 use the smaller value, 22, chosen from the two options 22 and 24 use the larger value, 24, chosen from the two options 22 and 24 use the smaller value, 21, chosen from the two options 21 and 23Q3 - Returns on stocks X and Y are listed below: Period 1 2 3 4 5 6 7Stock X 3% -2% 9% 6% -1% -4% 11%Stock Y 1% -4% 7% 12% 3% -2% -1% Consider a portfolio of 20% stock X and 80% stock Y. What is the (population) variance of portfolio returns? Please round your answer to six decimal places.Q3 - Returns on stocks X and Y are listed below: Period 1 2 3 4 5 6 7Stock X 5% 6% -2% -4% 6% 10% 7%Stock Y 1% -3% 6% 3% 12% 7% -5% Consider a portfolio of 40% stock X and 60% stock Y. What is the (population) variance of portfolio returns?Please round your answer to six decimal places.
- 1.- A study conducted in the automotive field states that more than 40% of vehicle engine failures are due to problems in the cooling system. To test this statement, a study is carried out on 70 vehicles and the critical region is defined as x < 26, where x is the number of vehicle engines that have problems in the cooling system. (use the normal approximation)a) Evaluate the probability of making a type I error, assuming that p = 0.4.b) Evaluate the probability of committing a type II error, for the alternative p = 0.3.A random sample of n1 = 14 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that σ1 = 19. For Englewood (a suburb of Denver), a random sample of n2 = 12 winter days gave a sample mean pollution index of x2 = 37. Previous studies show that σ2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. (a) Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (i) What is the level of significance?State the null and alternate hypotheses. H0: μ1 = μ2; H1: μ1 < μ2H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2H0: μ1 < μ2; H1: μ1 = μ2 (ii) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student's t. We assume that both population distributions are…Cardiovascular Disease Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2010. Fifteen new cases of MI were found. A- Of the 15 new MI cases in the preceding study, 5 died within 24 hours. Test whether the 24-hour case fatality rate changed from 2000 to 2010. B- Suppose we eventually plan to accumulate 50 MIcases during the period 2010–2015. Assume that the24-hour case-fatality rate is truly 20% during this period.How much power would such a study have in distinguishingbetween case-fatality rates in 2000 and 2010–2015 if atwo-sided test with significance level .05 is planned?
- In the daily production of a certain kind of rope, the number of defects per foot given by Y is assumed to have a Poisson distribution with mean ? = 4. The profit per foot when the rope is sold is given by X, where X = 70 − 3Y − Y2. Find the expected profit per foot.A random sample of n1 = 14 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that ?1 = 13. For Englewood (a suburb of Denver), a random sample of n2 = 10 winter days gave a sample mean pollution index of x2 = 35. Previous studies show that ?2 = 11. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. what is the sample test statistic find or estimate p valueFor the given Problem, suppose that the probability of concluding that the process is out of control when it is actually in control is set at .02. Find the upper and the lower control limits for the resulting X- chart.