Let X1, X2, ..., X10 be a random sample from a gamma distribution with a = 3 and B = 1/0. Suppose we believe that e follows a gamma-distribution with a = 3 and B = 2: What is the Bayes point estimate using the mode of the posterior distribution?

Referring to the example below If a compliance rate of 95% is expected how many of the 750 charts requested could fall below the standard and still be within the 95% goal An him department has 50,000 active records on file the record supervisor has established a maximum 15 minute time. For retrieval of a record during the past month 750 charts were requested of this number 688 where retrieved within a 15 minute. What percentage of the records fell below the established standard subtracting 688 from 750 indicates that 62 charts did not meet the required standard bus 62 out of 750 retrievals were not in compliance for an 8.27% non-compliance rate

The manufacturer of a new eye cream claims that the cream reduces the appearance of fine lines and wrinkles after just 14 days of application. To test the claim, 10 women are randomly selected to participate in a study. The number of fine lines and wrinkles that are visible around each participants eyes is recorded before and after the 14 days of treatment. The following table displays the results. Test the claim at the 0.02 level of significance assuming that the population distribution of the paired differences is approximately normal. Let women before the treatment be Population 2.      Before: 10, 11, 14, 11, 9, 11, 12, 14, 11, 14  After: 8, 11, 13 , 11, 5, 7, 13, 12, 8, 10  Question 1 : Compute the value of the test statistic. Round your answer to three decimal places. Additionally  Question 2: Draw a conclusion and interpret the decision.

Please do a, e, and f only

Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with s.d.= 2.3% . A random sample of 12 Australian bank stocks has a sample mean of x=6.16% . For the entire Australian stock market, the mean dividend yield is 7.2%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 7.2%? Find (or estimate) the P-value. Round your answer to three decimal places.

The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers?                                                                                                                                                                                                                                                                    Use α = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal.   Teacher 1 Teacher 2 ?̅1 =  473 ?̅2 = 459 S1 = 39.7 S2 = 24.5 n 1 = 8 n 2 = 18   a. State the null and alternate hypotheses (write it mathematically) and write your claim.   b. Find the test statistic        c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and…

Suppose a data set from a bike share company contains the number of daily bike rentals at each of 6 stations for the 23 weekdays of a particular month, i.e. we have Yij for i = 1, ..., 23 and j 1,...6. Write down a hierarchical normal model that can be used to estimate the mean number of bike rentals at each station. You can assume that the unknown variance o? of the number of bike rentals is the same for each station.

Let Y be the life in hours of a battery. Assume Y is normally distributed with mean 200 and variance o?. If a purchaser of such batteries requires that at least 90% of the batteries have lives exceeding 150 hours, what is the largest value o can be and still have the purchaser satisfied?

Suppose you are constructing a CI for a mean using T distribution and your sample size is 33. What would tge degree of freedom be for the t distribution that you would be using

The human resources department of a major corporation announced that the number of people interviewed by the corporation in one month has a mean of 101 and a variance, oʻ, of 266. The management of the corporation suspects that the variance exceeds 266. A random sample of 10 months yielded a mean of 105 interviews, with a variance of 378. If we assume that the number of people interviewed by the corporation in one month follows an approximately normal distribution, is there enough evidence to conclude, at the 0.1 level of significance, that the management's claim is correct? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H. :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO (c) Find the value of the test statistic. (Round…