You are given the following data on large business policyholders:(i)Losses for each employee of a given policyholder are independent and have a commomean and variance.(ii)The overall average loss per employee for all policyholders is 20.(iii)The variance of the hypothetical means is 40.(iv)The expected value of the process variance is 8000.(v)The following experience is observed for a randomly selected policyholder:Average Loss perEmployee15Number ofYearEmployees18002106005400Determine the Bühlmann-Straub credibility premium per employee for this policyholder.(A)Less than 10.5(B)At least 10.5, but less than 11.5(C)At least 11.5, but less than 12.5(D)At least 12.5, but less than 13.5(E)At least 13.5

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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what is the predicted number of sleep hours for persons with 60 years of age?
The community hospital is studying its distribution of patients. A random sample of 317 patients presently in the hospital gave the following information: Type of Patient Old rate of occurrences of the types of patients Present number of occurrences of these types of patients Maternity ward 20% 65 Cardiac ward 32% 100 Burn ward 10% 29 Children's ward 15% 48 All other wards 23% 75 Using a 5% level of significance, test the claim that the distribution of patients in these wards has not changed. Problem 1 (Test Statistic) A. χ2 = 0.036 B. χ2 = 315.36 C. χ2 = 0.355 D. χ2 = 1101.94 E. χ2 = 0.6322 Problem 2 (p-value, conclusion) A. p = 0.9965; RHo (Observed Values do not match Expectation) B. p = 0.9860; FRHo (Observed Values match Expectation) C. p = 0.9965; FRHo (Observed Values match Expectation) D. p = 0.9860; RHo (Observed Values do not match Expectation) E. p = 0.0035; RHo (Observed Values do not match Expectation)
Which of the following are the names commonly used for the variable Y in sample regression? 1. covariate variable 2. independent variable 3. predictor variable 4. Explained variable 5. Response variable 6. explanatory variable 7. Predicted variable 8. Dependent variable 9. Criterion variable
Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain. (Let 1 = Linda's rats, 2 = Tuan's rats and 3 = Javier's rats.) Weights of Student Lab Rats Linda's rats Tuan's rats Javier's rats 43.0 46.9 51.1 38.5 40.1 40.4 40.7 38.4 37.1 45.8 45.7 44.8 37.8 43.6 47.7 Part (a) State the null hypothesis. H0: ?1 = ?2 = ?3 H0: At least two of the group means ?1, ?2, ?3 are not equal. Part (b) State the alternative hypothesis. Ha: ?1 = ?2 = ?3 Ha: At least two of the group means ?1, ?2, ?3 are not equal. Part (c) Enter an exact number as an…
The accounting department analyzes the variance of the weekly unit costs reported by two production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.3 and 5.4, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of unit cost variance? Use ? = 0.10. State the null and alternative hypotheses. -H0: ?12 > ?22 Ha: ?12 ≤ ?22 -H0: ?12 ≠ ?22 Ha: ?12 = ?22 -H0: ?12 ≤ ?22 Ha: ?12 > ?22 -H0: ?12 = ?22 Ha: ?12 ≠ ?22 Find the value of the test statistic. (Round your answer to two decimal places.) statistic=?? Find the p-value. (Round your answer to four decimal places. Remember: When using WebAssign technology to find p-values, use the entire test statistic (not the rounded answer from the previous question.)) p-value = ?? State your conclusion. -Reject H0. We can conclude that there is a difference between the population variances. -Do not reject H0. We cannot conclude that…
(a) An indicator of the value of a stock relative to its earnings is its price-carnings ratio. The following table provides the summary statistics of the price-earnings ratios for a random sample of 24 stocks, 8 cach from the healthcare, financials and real estate sectors. Sector Sample mean Sample variance Sample size Healthcare 32.65 4.23 8 Financials 30.01 3.64 8 Real estate 8 29.24 4.27 You are also given that: 3 ΣΣ m = 22,657.84. j=1 i=1 Test at the 5% significance level whether the true mean price-carnings ratios for the three market sectors are the same. Use the ANOVA table format to summarise your calculations. You may exclude the p-value.
A stock analyst wondered whether the mean rate of return of financial, energy and utility stocks differed over the past 5 years. He obtained a simple random sample of eight companies from each of the three sectors and obtained the 5-year rates of return shown in the following table (in percents): Financial Energy Utilities 10.76 12.72 11.88 15.05 13.91 5.86 17.01 6.43 13.46 5.07 11.19 9.90 19.50 18.79 3.95 8.16 20.73 3.44 10.38 9.60 7.11 6.75 17.40 15.70 Source: Morningstar.com Required: (a) State the null and alternative hypothesis. (b) Are the mean rates of return different at the alpha = 0.05 level of significance? Please explain your answer, citing numeric and other evidence in support of your response.
Give a brief example of both a theoretical distribution of data.
5.Stocks and Mutual Fund Ownership It has been found that 51.4% of U.S. households own stocks and mutual funds. A random sample of 300 heads of households indicated that 178 owned some type of stock. At what level of significance would you conclude that this was a significant difference? Use the P-value method. Assume the variable normally distributed. Use a graphing calculator. Find the P-value. At what level of significance is this a significant difference?
You just finished statistics class and are eager to collect and analyze your own data! You run out and collect data on students' living arrangements (measured as either on-campus housing or off-campus housing) and whether they are involved in extra-curricular activities (measured as either involved or not involved). You want to examine whether there is an equal distribution of students who live on- and off-campus among those are are involved or not involved in extra-curricular activities. You will most likely use ___ to analyze your data. Group of answer choices a z-test a two-sample t-test a one-sample t-test an ANOVA a correlation a chi-square test a z-score a one-predictor regression a two-predictor regression
EXAMPLE 4.9 Students who seek therapy at university counseling centers often do not attend many sessions. For example, in one study, the median number of therapy sessions was 3 and the mean was 4.6 (Hatchett, 2003). Let’s examine the spread of fictional scores for a sample of five students: 1, 2, 4, 4, and 10 therapy sessions, with a mean of 4.2. We find out how far each score deviates from the mean by subtracting the mean from every score. First, we label with an X the column that lists the scores. Here, the second column includes the results we get when we subtract the mean from each score, or X − M. We call each of these a deviation from the mean (or just a deviation)—the amount that a score in a sample differs from the mean of the sample. X X − M 1 − 3.2 2 − 2.2 4 − 0.2 4 − 0.2 10 5.8 But we can’t just take the mean of the deviations. If we do (and if you try this, don’t forget the signs—negative and positive), we get 0—every time. Are you surprised?…
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given questions. Listed below are selling prices (dollars) of TVs that are 60 inches or larger and rated as a "best buy" by a popular magazine. Are the resulting statistics representative of the population of all TVs that are 60 inches and larger? If you decide to buy one of these TVs, what statistic is most relevant, other than the measures of central tendency? 1200, 1250, 1300, 1250, 1700, 1850, 1250, 1800, 1850, 1150, 1250, 1450

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