A furniture store claims that a specially ordered product will take, on average, u = 42 days (6 weeks) to arrive. The standard deviation of these waiting times is 7 days. We suspect that the special orders are taking longer than this. To test this suspicion, we track a random sample of 35 special orders and find that the orders took a mean of 43 days to arrive. Assume that the population is normally distributed. Can we conclude at the 0.05 level of significance that the mean waiting time on special orders at this furniture store exceeds 42 days? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. H, : H :0 (b) Determine the type of test statistic to use. D=D OSO (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) O
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- A manufacturer claims that the light bulbs that they produce have a mean lifetime of 1,200 hours and standard deviation of 400 hours. A random sample of size 50 is selected and the sample mean, , is calculated.A coin-operated drink machine was designed to discharge a mean of 9 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 15 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 9.13 fluid ounces and 0.22 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, μ, differs from 9 fluid ounces? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H Ho : 0 H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal…It was reported that last year the average price of gallons of gasoline in a city X was $3.15. This year a sample of 50 gas stations had an average price of $3.10 for a gallon. We assume that the population standard deviation of prices is $0.15. We are interested in determining whether this year's mean price is less than last year. Perform a hypothesis test at the level of significance α=0.05.
- 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).A furniture store claims that a specially ordered product will take, on average, u = 35 days (5 weeks) to arrive. The standard deviation of these waiting times is 8 days. We suspect that the special orders are taking longer than this, To test this suspicion, we track a random sample of 60 special orders and find that the orders took a mean of 36 days to arrive. Can we conclude at the 0.10 level of significance that the mean waiting time on special orders at this furniture store exceeds 35 days? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. Ho (b) Determine the type of test statistic to use. (Choose one) ▼ 自ロ OEx. Derive the MLE for a random sample from Exp(A) distribution that is subject to left truncation and right-censoring (LTRC); be sure to provide its variance estimate as well. Compare to the case where there is only right-censoring that we derived in the lecture notes earlier.A coin-operated drink machine was designed to discharge a mean of 8 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 22 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 8.11 fluid ounces and 0.19 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, μ, differs from 8 fluid ounces? Use the 0.05 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. : (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) (e)…The breaking strengths of cables produced by a certain manufacturer have a mean, u, of 1775 pounds, and a standard deviation of 95 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 20 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1796 pounds. Assume that the population is normally distributed. Can we support, at the 0.1 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.) Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: Н Н The alternative hypothesis: 口Sロ The type of test statistic: (Choose one) ロロ OAccording to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 46 months. A researcher for a consumer advocate group tests this by selecting 10 bulbs at random. For the bulbs in the sample, the mean lifetime is 42 months. It is known that the population standard deviation of the lifetimes is 4 months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the population mean lifetime, u, of light bulbs made by this manufacturer differs from 46 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. H₁ : 0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find…The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1875 pounds and a standard deviation of 70 pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength, µ, of the cables is now greater than 1875 pounds. To see if this is the case, 46 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1886 pounds. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the population mean breaking strength of the newly- manufactured cables is greater than 1875 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the…Suppose that there are two borrowing strategies from a commercial bank as short-term and long-term. We have two small samples (n1=8 and n2=8) and sampled populations are normal. Standard deviation for the first sample is 200 and for the second one is 150. The researcher wants to determine whether the variation in the customers preferring short-term borrowing differs from the variation in the customers preferring long-term borrowing. (Use 0.10 significance level)The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1775 pounds and a standard deviation of 70 pounds. The Español company believes that, due to an improvement in the manufacturing process, the mean breaking strength, µ, of the cables is now greater than 1775 pounds. To see if this is the case, 16 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1806 pounds. Assume that the population is normally distributed. Can we support, at the 0.10 level of significance, the claim that the population mean breaking strength of the newly- manufactured cables is greater than 1775 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. 00 Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) 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