4.2.19. Let X₁, X2..... X be a random sample from a gamma distribution with known parameter a = 3 and unknown 3 > 0. In Exercise 4.2.14, we obtained an approximate confidence interval for 3 based on the Central Limit Theorem. In this exercise obtain an exact confidence interval by first obtaining the distribution of 22{ X./β. Hint: Follow the procedure outlined in Exercise 4.2.18.
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- 6.4.5-T Assume that females have pulse rates that are normally distributed with a mean of u = 74.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute. The probability is 0.6255. (Round to four decimal places as needed.) b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 78 beats per minute. The probability is (Round to four decimal places as needed.)A movie studio wishes to determine the relationship between the revenue from the rental of comedies on DVD and videotape and the revenue generated from the theatrical release of such movies. The studio has bivariate data from a sample of 13 comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from DVD and videotape rentals (in millions of dollars) for each of the 13 movies. The least- squares regression equation computed from the data is y= 3.57+0.13x. The studio has plans for the DVD/video release of a comedy that grossed about 40.5 million dollars in theaters. The studio has predicted the rental revenue from this release using the regression equation and is now interested in both a prediction interval for this rental revenue and a confidence interval for the mean rental revenue of movies generating this same theater revenue. The studio has already computed the following for their data: • mean…9.3 Let Y₁, Y₂,..., Y, denote a random sample from the uniform distribution on the interval (0, 0+1). Let 0 =Y-; and O=Y). a Show that both ₁ and ₂ are unbiased estimators of 0. b Find the efficiency of 8₁ relative to ₂. n n+1
- 7.2.3. X is the continuous uniform (-5, 5) random variable. Given the event B = {|X| < 3}, find the (a) conditional PDF, fx|B(x), (b) conditional expected value, E[X|B], (c) conditional variance, Var[X|B].7.1-2A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.8 seconds. A random sample of 22 sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.09 seconds. At α=0.01 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed (a) Identify the claim and state H0 and Ha. b) THe claim is the _______ hypothesis. c) t= d) p= e) Decide whether to reject or fail to reject the null hypothesis. f) Interpret the decision in the context of the original claim.
- A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.8 seconds. A random sample of 24 sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.08 seconds. At α=0.10 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a) Identify the claim and state H0 and Ha. H0: muμ ▼ enter your response here Ha: ▼ sigma squaredσ2 muμ sigmaσ pp ▼ not equals≠ greater than or equals≥ greater than> less than< less than or equals≤ equals= enter your response here (Type integers or decimals. Do not round.) The claim is the ▼ alternative null hypothesis.Tests the claim that 1 # p2. Assume the samples are normally distributed, random and independent. of + o S1 =0.77 ; s2 = 0.82 E1 = 48.92 ; z2 = 48.94 n1 = 24; n2 = 31 a. Calculate the Standard Error s-, = (use 3 decimal places) (use 2 decimal places) b. Calculate the t-test statistic using the standard error from part a. t = c. What are the degrees of freedom? df %3! d. At a = 0.02, Use the distribution table to find the critical values for the rejection region t = ± (use 4 decimal places) e. What is your conclusion? O Fail to reject the null hypothesis and do not support the claim O Reject the alternative hypothesis and support the claim O Accept the null hypothesis and support the claim O Reject the null hypothesis and support the claim O Accept the alternative hypothesis and reject the claim7.4.15-T Question Help v A humane society claims that less than 73% of households in a certain country own a pet. In a random sample of 600 households in that country, 420 say they own-a pet. At a = 0.10, is there enough evidence to support the society's claim? Complete parts (a) through (c) below. (a) Identify the claim and state Ho and H Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. More than % of households in the country own a pet. O B. Less than % of households in the country own a pet. O C. The percentage households in the country that own a pet is not %. O D. % of households in the country own a pet. Click to select and enter your answer(s) and then click Check Answer. 4 parts remaining Clear All Check Answer 1:06 AM P Type here to search 2/21/2021 on fs 10 144 esc @ %23 %24 tbacksoace 3. 6. 7. 8. 9. W R Y tab H. K
- An individual who has automobile insurance from acertain company is randomly selected. Let Y be thenumber of moving violations for which the individualwas cited during the last 3 years. The pmf of Y is y p(y) 0 0.6 0.25 0.10 0.05 2 4 6 Suppose an individual with Y violations incurs a surcharge of $100. Calculate the standard deviation of the surcharge Y. 1.48 1.72 2.2 1.24.3.7Suppose that the time in minutes taken by a worker on an assembly line to complete a particular task has a gamma distribution with parameters k = 44 and λ = 0.7. (a) What are the expectation and standard deviation of the time taken to complete the task? (b) Use a software package to find the probability that the task is completed within an hour.An individual who has automobile insurance from acertain company is randomly selected. Let Y be thenumber of moving violations for which the individualwas cited during the last 3 years. The pmf of Y is MONTE 0 2 p(y) 0.6 0.25 0.10 0.05 6 Suppose an individual with Y violations incurs a surcharge of $100. Calculate the standard deviation of the surcharge Y. 1.48 1.72 2.2 01.2