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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- The patient's recovery time from a particular surgical procedure is normally distributed with a mean of 26 days and a standard deviation of 7.24 days. Let X - is the number of days a randomly selected patient needs to recover from the surgical procedure. What is the upper bound of 90% confidence interval of X?A random sample of size 30 from a normal population yields x̅ = 69 and s = 4. The lower bound of a 95 percent confidence interval is (Round off upto 2 decimal places).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.
- A sample of 66 night-school students' ages is obtained in order to estimate the mean age of night-school students. x = 24.7 years. The population variance is 18. (a) Give a point estimate for u. (Give your answer correct to one decimal place.) (b) Find the 95% confidence interval for u. (Give your answer correct to two decimal places.) Lower Limit Upper Limit (c) Find the 99% confidence interval for u. (Give your answer correct to two decimal places.) Lower Limit Upper LimitA random sample of 10 observations from population A has sample mean of 152.3 and a sample standard deviation of 1.83. Another random sample of 8 observations from population B has a sample standard deviation of 1.94. Assuming equal variances in those two populations, a 99% confidence interval for μA − μB is (-0.19, 4.99), where μA is the mean in population A and μB is the mean in population B. (a) What is the sample mean of the observations from population B? (b) If we test H0 : μA ≤ μB against Ha : μA > μB, using α = 0.02, what is your conclusion?X. is found to be 19.1, and the A simple random sample of sizen is drawn from a population that is normally distributed. The sample mean, sample standard deviation, s, is found to be 4.9. (a) Construct a 96% confidence interval about u if the sample size, n, is 39. (b) Construct a 96% confidence interval about u if the sample size, n, is 68. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about u if the sample size, n, is 39. How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample size is 14, what conditions must be satisfied to compute the confidence interval? (a) Construct a 96% confidence interval about u if the sample size, n, is 39. Lower bound: Upper bound: (Round to two decimal places as needed.) (b) Construct a 96% confidence interval about u if the sample size, n, is 68. Lower bound: ; Upper bound: (Round to two decimal places as needed.) How does increasing the sample…
- You have taken a random sample of sizen & 95of a normal population that has a population mean ofμ = 140and a population standard deviation ofo = 23. Your sample, which is Sample 1 in the following table, has a mean ofx = 141.3. (In the table, Sample 1 is indicated by "M1", Sample 2 by "M2", and so on.) (to) Based on Sample 1, plot the confidence intervals of80%and95%for the population mean. Use1,282as the critical value for the confidence interval of 80%and use1960 as the critical value for the confidence interval of95%. (If necessary, you can refer to a list of formulas .) • Write the upper limit and the lower limit on the graphs to indicate each confidence interval. Write the answers with one decimal place. • For the points (♦and ◆), write the population mean, μ = 140. 128.0 128.0 80% confidence interval 139.0 X Ś 150.0 150.0 128.0 128.0 95% confidence interval 139.0 X Ś 150.0 150.0An SRS of 400 high school seniors gained an average of x = 21.87 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation o = 48.66. We want to estimate the mean change in score µ in the population of all high school seniors. (a) Using the 68-95-99.7 Rule or the z-table (Table A), give a 95% confidence interval (a, b) for u based on this sample. (Enter your answers rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.) a: b: (b) Based on your confidence interval in part (a), how certain are you that the mean change in score u in the population of all high school seniors is greater than 0? O The upper endpoint of the interval is larger than 0, so we are 95% certain that the mean change in score in the population of all high school seniors is greater than 0. O We cannot be…Suppose a marketing company randomly surveyed 404 households and found that in 214 of them, the woman made the majority of the purchasing decisions. Construct a 90% confidence interval for the population proportion of households where the women make the majority of the purchasing decisions.p'=α2=zα2=Margin of Error: E=We are 90% confident that the proportion of households in the population where women make the majority of purchasing decisions is between___ and ___.
- A random sample of 11 items is drawn from a population whose standard deviation is unknown. The sample mean is x=920 and the sample standard deviation is s=25. Use Appendix D to find the values of student's tIn the past, students in a particular course have achieved a mean Xmas test score of 72.6, with a standard deviation of 12.5. This year, 15 students in one section achieved a mean Xmas test score of 72.2, while 10 students in another section achieved a mean Xmas test score of 77.3. Is the overall (grand) mean of the 25 students in this year's two sections significantly different from the mean obtained in previous years (α ≤ .05)?Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is ? = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.5. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. What is the level of significance?