Let X equal the length of life of a 60-watt light bulb marketed by a certain manufacturer. We do not know the distribution of X except that Var(X) = 1158. Let u be the mean of X. Suppose a random sample of n = 25 bulbs is tested until they burn out, yielding a sample mean of = 1368 hours. (i) Compute an approximate 95% confidence interval for u. (ii) Compute an approximate 95% one-sided confidence interval for that provides a lower bound for u, i.e. compute & such that
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- Find the Critical Values of the t- Distribution needed for a 95% confidence interval for the mean, with df=6. (that is find txα/2). Just type in the positive value, to 3 decimal places, in the text box below.A simple random sample of 10 subjects finds that the sample mean is 56 and the standard deviation is 4. Find the 98% confidence interval for u. Display the result in interval notation. You must round your result to decimal places. Remember that the information you have is from a small sample, you must use the t distribution. Remember that critical values can be calculated in EXCEL using the degrees of freedom (n-1) and the level of significance (I - C) as a function of T.INV 2T (Level of Significance, Degrees of Freedom) Select one: a. The interval is: (53,057, 58,943) b. The range is: (53,521, 58,479). c. The interval is: (51,080, 60,920) d. The interval is: (51.991, 60.009) e. The interval is: (52,431, 59,569)A random sample of 24 items is drawn from a population whose standard deviation is unknown. The sample mean is = 870 and the sample standard deviation iss= 25. Use Appendix D to find the values of Student's t. %3D (a) Construct an interval estimate of u with 98% confidence. (Round your answers to 3 decimal places.) The 98% confidence interval is from to (b) Construct an interval estimate of u with 98% confidence, assuming that s = 50. (Round your answers to 3 decimal places.) %3D The 98% confidence interval is from to (c) Construct an interval estimate of u with 98% confidence, assuming that s = 100. (Round your answers to 3 decimal places.) The 98% confidence interval is from to (d) Describe how the confidence interval changes as s increases. O The interval stays the same as s increases. < Prev 6 of 10 Next
- Suppose a certain species bird has an average weight of x = 3.2 grams. Based on previous studies we can assume that the weights of these birds have a normal distribution with sigma = 0.34 grams. For a small group of 18 birds , find a 98% confidence interval for the average weights of these birds. Write answer in interval notation with two decimal places.A simple random sample of 60 items resulted in a sample mean of 71. The population standard deviation is 13. a. Compute the 95% confidence interval for the population mean (to 1 decimal). Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals).In the past, a chemical company produced 880 pounds of a certain type of plastic per day. Now, using a newly developed and less expensive process, the mean daily yield of plastic for the first 50 days of production is 871 pounds; the standard deviation is 21 pounds. Do the data provide sufficient evidence to indicate that the mean daily yield for the new process is less than that of the old procedure? (Use α=0.05) (a) Alternative hypothesis for the problem above is μ 871 Ομ 880 <
- 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.The ages of registered voters in Smith County are normally distributed with a population standard deviation of 3 years and an unknown population mean. A random sample of 18 voters is taken and results in a sample mean of 55 years. Find the margin of error for a 95% confidence interval for the population mean. z0.10z0.10 z0.05z0.05 z0.025z0.025 z0.01z0.01 z0.005z0.005 1.282 1.645 1.960 2.326 2.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.
- Suppose X1,..., Xn is a random sample from an exponential distribution with mean e. If X = 17.9 with n = 50, find (a) a one-sided 95% confidence interval for 0, and (b) a two-sided 95% confidence interval for 0.In the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?A researcher collected sample data for 19 middle-aged women. The sample had a mean serum cholesterol level (measured in milligrams per one hundred milliliters) of 190.3, with a standard deviation of 9.5. Assuming that serum cholesterol levels for middle-aged women are normally distributed, find a 95% confidence interval for the mean serum cholesterol level of all women in this age group. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit= Upper limit=