(i) Annual claim frequency for an individual policyholder has mean 2 and variance c (ii) The prior distribution for 2 is uniform on the interval [0.5, 1.5]. (iii) The prior distribution for o? is exponential with mean 1.25. A policyholder is selected at random and observed to have no claims in Year 1. Using Bühlmann credibility, estimate the number of claims in Year 2 for the selected policyholder. (A) 0.56 (B) 0.65 (C) 0.71 (D) 0.83 (E) 0.94
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- The second picture is the minitab outcome as asked to be used in the question.Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 15 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.Solve for the:1. Mean2. Median3. Mode 4. Standard Deviation
- There are 2000 persons living in a certain locality whose monthly income is normallydistributed with mean 800 and variance 22500. Find the number of persons whose income is:(i) Above 1200(ii) Below mean(iii) Between 300 and 1200(iv) Outside the range, 300 and 1200The diameter of a cylinder follows a normal distribution with the mean of 10cm and the variance of 0.04 cm². (a) Construct a Shewhart chart to monitor the process mean of cylinder diameter with a sample size 4? (Use L=3) (b) If the mean of the process changes to 10.5 cm, what is the probability that you detect this mean shift at the immediate next sample (the first sample after the mean shift)? (c) Continue b), what is the probability of detecting this mean shift before plotting the 5th sample after the mean shift?What would be the appropriate inferential statistic to evaluate the relationship between: • 'Generation' [Baby Boom (1946-1964), Generation X (1965-1980), Millennials (1981-1996)] • 'Household Income' (in US $) median and interquartile range means comparison (t or ANOVA) correlation coefficient (r) chi-square (x2) mean and standard deviation frequency and percentage
- The week before the bill to repeal Obamacare came up for consideration in the Senate, one polling agency increased the size of the random sample of U.S. adults they surveyed on this issue from 500 to 1500. What effect would this increase have on the polling agency's estimate of the proportion of U.S. adults in favor of repealing Obamacare, assuming the true proportion in favor remained constant? (A) A reduction in the variability of the estimate (B) An increase in the variability of the estimate (C) A reduction in the bias of the estimate (D) An increase in the bias of the estimate (E) A reduction in both the variability and the bias of the estimateQ1. Using 625 trading days of data, you estimated the daily log return follows a normal distribution with a mean of 5 bps and and a stdev of 125 bps. Q1b. what is the 90, 95, and 99% confidence interval for your mean return estimate?In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?
- For each of these questions, choose the option (A, B, C or D) that is TRUE. 1. The range of a sample gives an indication of the (A) way in which the values cluster about a particular point (B) number of observations bearing the same value (C) maximum variation in the sample (D) degree to which the mean value differs from its expected value. 2. The observation which occurs most frequently in a sample is the (A) median (B) mean deviation (C) standard deviation (D) mode 3. What is the median of the sample 5, 5, 11,9, 8, 5, 8 ? (A) 5 (В) 6 (C) 8 (D) 9Assume blood-glucose levels in a population of adult women are approximately normally distributed with mean 90 mg/dL and standard deviation 13 mg/dL. - Suppose the "abnormal range" were defined to be glucose levels outside of 1 standard deviation of the mean (i.e., either at least 1 standard deviation above the mean, or at least 1 standard deviation below mean). What percentage of individuals would be called "abnormal" and need to be retested?Assume that the following satisfaction scores of three companies for the 4th quarter of 2010 and 2011 were obtained from the Rochester's Customer Satisfaction Index. Assume that the scores are based on a poll of 100 customers from each company. Because the polling has been done for several years, the standard deviation can be assumed to equal 7 points in each case. (The scores on the following table are hypothetical values for the exam only) Company Costco BJ's Sam's 2010 Score 73 Ha: μ 1-μ 2 > 0 Ho: μ 1-μ 2 > 0 Ho: u 1-μ2=0 none of the above- Ha: μ 1-μ 2 <0 75 77 2011 Score 75 77 79 Professor Pan is interested in knowing whether the difference in the satisfaction score for Costco from 2010 to 2011 is statistically significant. assume a=5%, Professor Pan came up with the following hypotheses. Which of the following null or alternative hypotheses is correct?