Suppose we are trying to measure some physical constant . Assume that each time w easure µ, there is a small, independent random error ~ N(0, 0²) with o = 0.01. (i) How many measurements do we need to construct a 99% confidence interval of lengt 0.01 for u? (ii) If we can only afford to make only 10 measurements, what level of confidence can w achieve for a confidence interval of length 0.01?
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- A random sample of size 32 is selected from population X, and a random sample of size 43 is selected from population Y. A 90 percent confidence interval to estimate the difference in means is given as (−1.25,0.87). Consider a change in the sample sizes such that a random sample of size 52 is selected from population X and a random sample of size 63 is selected from population Y. When all other things remain the same, what effect would such a change have on the interval?The standard deviation of the measurements made by a special thermocouple is assumed to be 0.005 ° C.If the standard deviation of a sample of 45 thermocouples is 0.01, perform a hypothesis test with alpha = 0.01A random sample of size 32 is selected from population X, and a random sample of size 43 is selected from population Y. A 90 percent confidence interval to estimate the difference in means is given as (−1.25,0.87)(−1.25,0.87). Consider a change in the sample sizes such that a random sample of size 52 is selected from population X and a random sample of size 63 is selected from population Y. When all other things remain the same, what effect would such a change have on the interval? A) The width of the interval will increase. B) The width of the interval will decrease. C) The interval will contain no negative numbers. D) The level of confidence will increase. E) The sample means will increase.
- The pulse rates of 176 randomly selected adult males vary from a low of 40 bpm to a high of 116 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 95% confidence that the sample mean is within 2 bpm of the population mean. Assume that o= 10.1 bpm, based on the value s = 10.1 bpm from the sample of 176 male pulse ratesA random sample of 430 observations produced a sample proportion equal to 0.33. Find the critical and observed values ofzforth following test of hypotheses using alpha = 0.1 . H_{0} / p = 0.30 versus H_{1} / p > 0.30 .Sony would like to test the hypothesis that the average age of a PlayStation user (mu 1) is greater than the average age of an Xbox user (mu 2). A random sample of 36 PlayStation users had an average age of 34.2 years while a random sample of 30 Xbox users had an average age of 32.7 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.9 and 4.0 years, respectively. Sony would like to set alpha = 0.01. The critical value is ________ and the null hypothesis should _______. Select one: a. -2.33; be rejected. b. 2.33; not be rejected. c. 1.96; be rejected. d. 1.645; not be rejected.
- The analyst tells you that the returns on its shares in company XYZ have no systematic risk, in other words that the returns on its shares are completely unrelated to movements in the market. The value of beta and its standard error are calculated to be 0.428 and 0.372, respectively. The model is estimated over 76 observations. Write down the null and alternative hypothesisThe sample mean and standard deviation from a random sample of 30 observations from a normal population were computed as x¯=31x¯=31 and s = 9. Calculate the t statistic of the test required to determine whether there is enough evidence to infer at the 3% significance level that the population mean is greater than 28. Test Statistic =Based on a random sample of 25 units of product X, the average weight is 102 lbs., andthe sample standard deviation is 10 lbs. We would like to decide if there is enough evidenceto establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.what is the critical value to test the claim at (alpha)= ,01?
- It is desirable to test Ho (Null Hypothesis): Mu = 100 lb against H1: Mu <100 lb, based on the weights of a random sample of size n = 40 freight packages per truck.The population has: Image 1 For what values of X-Bar should Ho be rejected, if the probability of a type I error is alpha = 0.01?A sample of size n = 20 is drawn from a normal population. Find the critical value tα/2 needed to construct a 99% confidence interval.A statistician claims that the standard deviation of the weights of firemen is more than 25 pounds. A sample of 20 randomly chosen firemen had a standard deviation of their weights of 26.2 pounds. Assume the variable is normally distributed. At alpha=0.05 what is the critical value χ2 for this test?