Suppose that a random sample X₁, X2, X20 follows an exponential distribution with parameter B. Check whether or not a pivotal quantity exixts, if it exists, find a 100(1-a) % confidence interval for B.
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- A hypothesis test was performed to decide whether the mean number of words spoken per day by men is fewer than for women. αα = 0.05 and p = 0.02. If a man and a woman are randomly selected there is a 2% chance that the man will speak fewer words than the woman on that day.A sample of 20 items provides a sample standard deviation of 4.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.
- Suppose that X1, X2, X3 and X4 are all independent random variables, each with a normal distribution with mean 9 and variance 25. Define X-bar = (X1 + X2 + X3 + X4) / 4. Find Prob(X-bar > 10).An apple orchard farmer wants to know the true population proportion of all apples harvested at their farm which have the less valuable condition of being blemished, or in other words, are cider apples. This true population proportion is a parameter value represented by the symbol p. As a population parameter, this value can never be known with certainty. It can however, be estimated with varying levels of confidence. To estimate this parameter p, the farmer draws a simple random sample (SRS) of 524 apples from the orchard. Within this sample, the farmer finds that exactly 47 of the apples are cider apples. The farmer then computes a 96%-level confidence interval estimate for the parameter p. In percentage form, and rounded to four digits past the decimal point: What is the approximate value of the Lower Limit of this confidence interval? Include a percentage symbol at the end of your numerical answer (with no spaces).A manufacturer of MP3 players conducts a set of comprehensive tests on the electrical functions of its product. All MP3 players must pass all tests prior to being sold. Of a random sample of 1000 MP3 players, 30 failed one or more tests. Find a 99% confidence interval for the proportion of MP3 players from the population that pass all tests.
- In the study cited in Exercise 5.3.4, researchers found the mean sodium intake in men and women 60 years or older to be 2940 mg with a standard deviation of 1476 mg. Use these values for the mean and standard deviation of the U.S. population and find the probability that a random sample of 75 people from the population will have a mean: (a) Lessthan2450mg (b) Over3100mg(c) Between2500and3300mgIn a random sample of 29 residents living in major cities on the West Coast (Group 1) and 29 residents living in major cities on the East Coast (Group 2), each individual was asked their age. The results can be seen in the table below. The population standard deviation of the age in West Coast cities is known to be 11.2 years and in East Coast cities is known to be 9.3 years. Assume the populations are normally distributed. Run a test at a 0.05 level of significance to test if west coast cities are, on average, older. West Coast (Group 1) East Coast (Group 2) 25 34 47 45 18 37 38 20 30 19 50 26 52 79 61 46 40 29 22 55 34 23 35 35 55 36 60 51 68 41 20 50 33 32 36 38 37 26 42 44 60 19 71 28 54 27 20 18 45 30 52 20 34 22 57 43 64 62 Enter the P-Value - round to 4 decimal places. Make sure you put…How large of a sample is required for a to construct a 99% confidence interval around a mean with an error of less than 1.5. Assume the standard deviation is 42.
- A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. She randomly selected 54 men and 70 women to participate in the study. Each subject was required to step up and down a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained. Two sample T for Men vs Women N Mean StDev SE Mean Men Women 98% CI for mu Men - mu Women (- 12.20, - 1.00) T-Test mu Men = mu Women (vs H2 O C. Ho: H1 = H2; Ha: H1 #H2 (b) Identify the P-value and state the researcher's conclusion if the level of significance was a = 0.01. What is the P-value? P-value =A company manufactures tonnis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the balls bounce upward to be 54.7 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between -to ak and t as then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height of the sample is 56.8 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? Find -th os and to 96- -to.96 = 0.96 = (Round to three decimal places as needed.)Use Table B to find the critical value t* that should be used in constructing a 98% confidence interval based on a simple random sample of size n = 29 for the population mean. Assume the conditions are met. options t* = 2.467 t* = 2.326 t* = 2.462 None of these is correct.