Suppose that a random sample X₁, X₂,...,X20 follows an exponential distribution with parameter ß. Check whether or not a pivotal quantity exixts, if it exists, find a 100(1 – α)% confidence interval for ß.
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- A distribution with a mean of µ = 41 and a standard deviation of σ = 4 is transformed into a standardized distribution with µ = 100 and σ = 20. Find the new, standardized score for each of the following values from the original population. Original X = 39 Transformed X = Original X = 36 Transformed X = Original X = 45 Transformed X = Original X = 50 Transformed X =A company manufactures tennis 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.95 and to.95, 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 56.9 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptable tennis balls? 0 Find -to.95 and to.95. -¹0.95 = ¹0.95 (Round to three decimal places as needed.) =A population has population mean = 60 and population standard deviation = 10. Find the z-score corresponding to each of the following sample means: A sample of n = 4 with M = 55. A sample of n = 25 with M = 64 A sample of n = 100 with M = 62
- Suppose a random sample of adult women has a sample mean height of x¯=64.3 inches, with a sample standard deviation of s=2.4 inches. Since height distribution are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two heights are approximately 99.7% of the data?Let X1, X2,..., X3 denote a random sample from a population having mean u and variance o?. Which of the estimators have a variance of 04A company is doing a hypothesis test on the variation in quality from two suppliers. Both distributions are normal, and the populations are independent. Use a = 0.01. A sample of 22 products were selected from Supplier 1 and a standard deviation of quality was found to be 5.2696. A sample of 27 products were selected from Supplier 2 and a standard deviation of quality was found to be 3.8328. Test to see if the variance in quality for Supplier 1 is larger than Supplier 2. What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem. Ho: Select an answer ? v Select an answer H1: Select an answer v Select an answer Based on the hypotheses, compute the following: Round answers to at least 4 decimal places. The test statistic is = The p-value is = The decision is to Select an answer v that the variance in The correct summary would be: Select an answer quality for Supplier 1 is larger than Supplier 2.
- The Wilcoxon signed-rank test can be used to perform a hypothesis test for a population median, η, as well as for a population mean, μ. Why is that so?A chain of taco restaurants claims that the population mean of the wait times in their drive-thru for all customers is minutes. You work for a competitor and you want to test that claim. To do so, you select a random sample of 40 of the chain's drive-thru customers and record the wait time in the drive-thru for each. Assume it is known that the population standard deviation of the wait times in the drive-thru for the taco chain's restaurants is 2.79 minutes. Based on your sample, follow the steps below to construct a 99% confidence interval for the population mean of the wait times in the drive-thru for all customers. Then state whether the confidence interval you construct contradicts the restaurant chain's claim. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 40 customers. Take Sample Sample size: 0 Point estimate: Population standard deviation: 0 Enter the values of the sample size, the point estimate for the…Suppose that for the past several decades, daily precipitation in Seattle, Washington has had a mean of 2.4 mm and a standard deviation of 11.4 mm. Researchers suspect that in recent years, the mean amount of daily precipitation has changed, so they plan to obtain data for a random sample of 195 days over the past five years and use this data to conduct a one-sample ?z‑test of ?0:?=2.4H0:μ=2.4 mm against ?1:?≠2.4H1:μ≠2.4 mm, where ?μ is the mean daily precipitation for the last five years. Although they realize that rainfall does not follow a normal distribution, they feel safe using a ?z‑test because the sample size is large. The researchers want to know what the power of this test is to reject the null hypothesis at significance level ?=0.05α=0.05 if the actual mean daily precipitation is 2.6 mm or more. Computing power by hand requires two steps. The first step is to use a significance level of 0.05 to determine the values of the sample mean for which they will reject their null…
- An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).Let x be a random variable that represents the pH of CVS brand water. The mean of this x distribution is u = 6.5 pH. A new company wants to sell its water at CVS locations. However, CVS management believes that the new brand will have a mean pH different from the CVS brand water. A random sample of 70 water samples were taken from this new company's water and it was found that the sample mean was 7.2 pH and the sample standard deviation was s = 2.5 pH. Do the data indicate that the new company's water has a mean pH level greater than 6.5, which is the pH of the CVS brand water? Use a 5% significance level. Identify the following in your answer. 1. Identify the null hypothesis Ho and alternate hypothesis H1 for the problem. 2. Identify and test statistic, the p-value and the calculator key used. Test Statistic (t): (Round to three decimal places) = p - value: (Round to four places) = Calculator key used: 3. Identify the significance level and determine if you reject or fail to reject…Consider a normally distributed population of scores with a mean μ = 100 and σx = 10. What score has a Z value of -0.82?
