Let X1, X2, ..., Xn be a random sample from f(x;0) = 0e-I(0,00)x). Find a 100y or %3D (1– a)100 percent confidence interval for the mean of the population.
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- Random samples are obtained from two normal populations with equal variance of o? = 18. If the sample sizes are 11 and 9, respectively, find the 95th percentile of the ratio of the sample variances (round off to second decimal place).A Random Sample Of Size 25 Is To Be Selected From A Normal Population Having A Mean Of 81 And A Variance Of 9. What is the 95th percentile of the sampling distribution of the mean?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…
- The acceptable level for insect filth in a certain food item is 2insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 50 ten-gram portions of the food item is obtained and results in a sample mean of x=2.5 insect fragments per ten-gram portion. Complete parts (a) through (c) below.A study was conducted using 39 undergraduates at a large private university who volunteered to participate in the research as partial fulfillment of a course requirement. One of the items studied was the maximum daily amount of alcohol consumed in the last month. Based on the data in the following table, is there a difference between males and females in the maximum amount of alcohol consumed in any one day in the past month? Use α = 0.05 and assume that the population variances are equal. Group Mean () Standard Deviation (s) Size of Sample (n) Males 8.2 5.9 17 Females 5.6 5.7 22 During the Saint Louis University Foundation Day, the Director of Physical Education recorded the mean height of 37 male students who showed average participation was 70.3 inches with inches, while 32 male students who showed no interest in participation had a mean height of 69.1 inches with inches. Is the director justified that male students who showed average…A random sample of 25 students obtained a mean of 78 and a variance of s2 = 15 on a college entrance exam in engineering. Assuming the scores are normally distributed, construct a 98% confidence interval of σ2
- (Mathematical Statistics) Let X1,X2,...,X5 be a random sample of the Gamma distribution with parameters a = and ß = 0, e > 0. Determine the 95% confidence interval for the parameter e based on the statistic E(i=1 - 5) Xi. 2A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x, be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x, be the empathy = 68.36. Another random sample of 31 fathers gave score of a father. A random sample of 37 mothers gave a sample mean of x, X, = 60.06. Assume that o, = 11.55 and o, = 11.45. (a) Let u, be the population mean of x, and let u, be the population mean of x,. Find a 99% confidence interval for u, - Hz. (Round your answers to two decimal places.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level? Because the interval contains only…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 9520 observations, the sample mean interval was x1 = 62.8 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 23,117 observations, the sample mean time interval was x2 = 73.0 minutes. Historical data suggest that ?1 = 8.98 minutes and ?2 = 12.83 minutes. Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. (a) Compute a 90% confidence interval for ?1 – ?2. (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…
- A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x1 be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x2 be the empathy score of a father. A random sample of 38 mothers gave a sample mean of x1 = 69.04. Another random sample of 31 fathers gave x2 = 57.68. Assume that ?1 = 11.27 and ?2 = 11.16 (a) Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. Find a 99% confidence interval for ?1 – ?2. (Round your answers to two decimal places.) lower limit= upper limit=The sales manager of a large company selected a random sample of n = 10 salespeople and determined for each one the values of x = years of sales experience and y = annual sales (in thousands of dollars). A scatterplot of the resulting (x, y)pairs showed a linear pattern.(a)Suppose that the sample correlation coefficient is r = 0.75 and that the average annual sales is y = 100.If a particular salesperson is 2 standard deviations above the mean in terms of experience, what would you predict for that person's annual sales?Since the value for experience is 2 standard deviations above the mean experience, you can predict annual sales will be ________________standard deviations above the mean annual sales.(b)If a particular person whose sales experience is 1.7 standard deviations below the average experience is predicted to have an annual sales value that is 1 standard deviation below the average annual sales, what is the value of r? (Round your answer to two decimal places.)r =Let X1, ..., Xn be a sample from a geometric random variable with parameter p.(a) Find the maximum likelihood estimator for p.(b) Is the estimator unbiased?(c) Is the estimator consistent?
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