3. Let X1, X2, ..., X, be a random sample from a normal population with mean u and variance a2 taken independently from another random sample Y1, Y2, Ym from a normal population with mean 0 and variance o?. Let Z; = ACP, Derive the distribution of T =- m-1
Q: 42. Consider the random variable (X, Y) of Exercise 9. (a) Find the curve of regression of X on Y.…
A: Detailed explanation:Regression Curves and Conditional Expectation:In statistics, regression…
Q: Executives of a supermarket chain are interested in the amount of time that customers spend in the…
A: We are given that the mean shopping time spent by customers at the supermarkets is The sample mean…
Q: A random variable X has a binomial distribution with = 0.34 and a sample size of n. Find the mean…
A:
Q: Let Y, represent the ith normal population with unknown mean , and unknown variance of for i=1,2.…
A: Given that the random variable represent the ith normal population with unknown mean and unknown…
Q: Suppose a continuous random variable X pdf constant from 0 to 7.516, where the pdf is zero…
A: Suppose a continuous random variable X pdf constant from 0 to 7.516, where the pdf is zero…
Q: The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National…
A: From the provided information,
Q: The average duration of labor from the first contraction to the birth of the baby in women over 35…
A: As per guidelines we will solve first question only, please repost other questions for more answers.…
Q: The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National…
A: The 99% confidence interval for μ1 – μ2 is obtained below: From the given information, the sample…
Q: The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National…
A: We have given that Sample size n1= 8860 , n2 = 23351 Sample mean xbar1 = 64.8 , xbar2 = 70.0…
Q: he U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National…
A: Solution: Given information: n1= 8860 Sample size of sample 1n2= 23351 Sample size of sample 2x1=…
Q: Executives of a supermarket chain are interested in the amount of time that customers spend in the…
A: It is given that confidence level is 0.99, the standard deviation is 27, and margin of error E is 4.
Q: The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National…
A: Sample size n1= 9440 , n2= 24.053 Sample mean xbar1 = 63.6 ,xbar2 = 72.8 Population standard…
Q: The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National…
A: Given: x¯1=61.4x¯2=72.4σ1=8.70σ2=12.55n1=9140n2=25106 Let μ1 be the population mean of x1 and let μ2…
Q: A population, T is normally distributed with unknown mean, u and variance 49. A sample of size 9…
A: Given : Population variance (σ2) = 49 Sample size (n) =9 Sample mean (X¯) = 20 Confidence level =…
Q: (a) Compute a 95% confidence interval for u, - Hz. (Use 2 decimal places.) lower limit upper limit…
A: Given that For years 1948 to 1952, sample size n1 = 8800, sample mean = 64.0, population SD = 8.35…
Q: (HC) adult standard deviation. A random sample of ten healthy adult females was taken with the…
A: Comment: As per the our company guidelines we are supposed to answer only three subparts. Kindly…
Q: Suppose the weights (in pounds) of eight rowers on each of the Cambridge and Oxford crew teams are…
A: To test the hypothesis that the mean weights of the populations of rowers on the Cambridge and…
Q: Carboxyhemoglobin is formed when hemoglobin is exposed to carbon monoxide. Heavy smokers tend to…
A: Part a: From the given data we have: S.No. X x-xbar 1 9.1 2.1025 2 9.8 0.5625 3 10.6…
Q: Suppose Y is a normally distributed random variable and Y=In(5X²). It is known that the mean and…
A: Given that is a normally distributed random variable, and .The mean and standard deviation of are…
Q: The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National…
A: We have given that Sample size n1= 8860 , n2= 24170 , Sample mean x1= 61.4 , x2= 70.6 , sigma1=…
Q: Let X1, X2, · .. ,Xn be i.i.d. samples distributed according to Geo(q). Consider the sample mean as…
A: Answer is given using concept of iid and expectation. please find solution below:
Q: Let Y, represent the ith normal population with unknown mean #, and unknown variance of for i=1,2.…
A: Given that the random variable represent the ith normal population with unknown mean and unknown…
Q: Parts (a) and (b) are both related to normal distribution but are not directly connected to each…
A: a)Mean= -1 , Standard deviation = 2
Q: REM (rapid eye movement) sleep is sleep during which most dreams ocour. Each night a person has both…
A: The given values are n1=11,x¯1=2.5,σ1=0.6,n2=11,x¯2=1.90,σ2=0.5.
Q: The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National…
A:
Q: dataset x = (x1, … , xn ) has sample variance of 0 when (n≥2 ). prove that all the data points are…
A: This problem is based on the sample variance and data sets. To show - If sample variance is zero…
Q: Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful…
A: Given : Let x1 be a random variable that represents the time interval (in minutes) between Old…
Q: The US Geological Survey complied historical data about Old Faithful Geyser from 1870 to 1987. Let…
A: To compute: 95% confidence interval for u1-u2. (use 2 decimal places)
Q: The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National…
A: Given information- We have given two independent populations. n1 = 9060, X1-bar = 62.4 minutes, σ1 =…
Step by step
Solved in 2 steps with 1 images
- Let X1, X2,...Xn be a random sample from a Poisson distribution with variance 0. Find a sufficient estimator for 0 and an unbiased estimator for 0 based on the sufficient estimator.call WnThe U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9060 observations, the sample mean interval was x1 = 62.4 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 24,638 observations, the sample mean time interval was x2 = 70.8 minutes. Historical data suggest that σ1 = 8.07 minutes and σ2 = 11.57 minutes. Let μ1 be the population mean of x1 and let μ2 be the population mean of x2. (a) Compute a 90% confidence interval for μ1 – μ2. (Use 2 decimal places.) lower limit upper limitThe U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9240 observations, the sample mean interval was x1 = 63.6 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 24,170 observations, the sample mean time interval was x2 = 69.2 minutes. Historical data suggest that σ1 = 8.00 minutes and σ2 = 12.62 minutes. Let μ1 be the population mean of x1 and let μ2 be the population mean of x2. (a) Compute a 99% confidence interval for μ1 – μ2. (Use 2 decimal places.) lower limit upper limit
- How would you figure out this problem for (a,b,c,d)?Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 62.0 kg and standard deviation ? = 9.0 kg. Suppose a doe that weighs less than 53 kg is considered undernourished. (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 70 does should be more than 59 kg. If the average weight is less than 59 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 70 does is less than 59 kg (assuming a healthy population)? (Round your answer to four decimal places.) Suppose park rangers captured, weighed, and released 70 does in December, and the average weight was x = 63.8 kg. Do you think the doe population is undernourished or not? Explain. A. Since the sample average is above the mean, it…What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? |Ho: µ is ? |H: µ is ? In the context of this test, what is a Type II error? V? v when, in A Type II error is ? fact, u is ? | the hypothesis that u is ? Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making? ?
- The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9180 observations, the sample mean interval was x1 = 62.6 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 24,872 observations, the sample mean time interval was x2 = 70.0 minutes. Historical data suggest that σ1 = 8.91 minutes and σ2 = 11.78 minutes. Let μ1 be the population mean of x1 and let μ2 be the population mean of x2. (a) Compute a 95% confidence interval for μ1 – μ2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…Let x1, x2, . . . , x100 denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean 75 lbs and variance 1 lb2. Let x be the sample mean weight (n = 100). (a) Describe the sampling distribution of x. The distribution is approximately normal with a mean of 75 lbs and variance of 1 lb2.The distribution is approximately normal with a mean of 75 lbs and variance of 0.01 lbs2. The distribution is unknown with a mean of 75 lbs and variance of 0.01 lbs2.The distribution is unknown with a mean of 75 lbs and variance of 1 lb2.The distribution is unknown with unknown mean and variance. (b) What is the probability that the sample mean is between 74.65 lbs and 75.35 lbs? (Round your answer to four decimal places.) P(74.65 ≤ x ≤ 75.35) = (c) What is the probability that the sample mean is greater than 75 lbs?Let x¡, denote a series of n numbers {x;: i=1,2,..,n}: Assume that x; is drawn from a distribution that is N(ux, ož). Show that the sample mean x = E, xị has a variance of ož/n carefully stating any required assumptions i. 1 at each step. ii. Show that the sample mean is an unbiased estimator of ux.
- Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, u, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate u. Assuming that the standard deviation of the population of shopping times at the supermarkets is 27 minutes, what is the minimum sample size she must collect in order for her to be 99% confident that her estimate is within 5 minutes of u? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.) ?Let X1, X2,..., Xn be a random sample of size n > 3 from a normal distribution with unknown mean μ and known variance equal to 2. Show that is an unbiased estimator of μ and compute its variance. p2. Cytomegalovirus (CMV) is a (generally benign) virus that infects one – half of young adults. If a random sample of 10 young adults is taken, find the probability that between 30% and 40% (inclusive) of those sampled will have CMV. Use the normal approximation with the continuity correction.
