IF n < 30 AND T = SHOW HOW THE 100(1-2a) % CONFIDENCE INTERVAL FOR μ IS DERIVED
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A: Option A is correct.
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A: Given information: The confidence level is 95%.
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- If the random sample X1,..., X, is taken from a normal distribution with mean value u and standard deviation o, then regardless of the sample size n, the sample mean X is distributed with expected value and standard deviation If a confidence level of 95% is used to construct a confidence interval for the mean u of a normal distribution when the value of standard deviation o is known, the z critical value is Standard error of an estimator ô is the of ê. error consists of rejecting the null hypothesis H, when H, is true. The area under a chi-squared curve with 10 degrees of freedom, which is captured between the two critical values X/2 and x-a/2 isTrue or False. Provide explanation!3. Time intervals (in minutes) X₁,..., Xn between successive eruptions of a geyser are modeled as X₂ Exponential (A), where A (> 0) is the eruption rate per minute. We want to report a plausible range for the median interval time. (d) 0 Find the MLE of A. (b) (c) Construct an approximate 95% confidence interval for A using the asymptotic distri- bution of AMLE. (Hint: use the approximation method for confidence interval) i.i.d. N = The median of the Exponential(A) distribution, denoted by 8, is a function of A as (log 2)/λ 0.693/A. Calculate an approximate 95% confidence interval for the median interval time using the Delta method. Find the Fisher information of A. -
- A population is distributed with a known standard deviation, σ = 18 units. A random sample of size 35 is obtained from this population. The mean of this sample is 70. True or False: Since the sample size is greater than 25 the distribution of sample means from this population should be approximately normally distributed. What is the lower limit of the 95% confidence interval for the population mean μ? (2 dp) What is the upper limit of the 95% confidence interval for the population mean μ? (2 dp). Based on your confidence interval, would you believe that the true mean of this population could be 75?A 100(1 - α)% confidence interval for the mean μ of a normal population when the value of σ is known is given by (x-²a/2" Six+ .za/2 VM). By how much must the sample size n be increased if the width of the CI above is to be halved? Halving the length requires n to be increased by a factor of If the sample size is increased by a factor of 16, what effect will this have on the width of the interval? Increasing the sample size by a factor of 16 will ---Select-- the length by a factor of ---Select-- increase Need Help? Read It decreaseIf n=520 and ˆpp^ (p-hat) = 0.4, construct a 98% Confidence Interval.In order to use technology, you need to compute the number of successes:x = n*ˆpp^Give your answers to three decimals. ________< p < __________
- If n=16, ¯xx¯(x-bar)=35, and s=17, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population.Give your answers to one decimal place. I used the formula 35-NORM.INV(1-2.0/2,0,1)*((17)/SQRT(16)) for the lower and the same but with a plus sign for the upper, I got it wrong and dont understand why. We have to use Excel so please explain what excel formula to use.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)?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 ɛ P(X - ≤ μµ)≈ 0.95.
- 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 ___.1. 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) (d) Conclusion of the test above is Reject the null hypothesis and the mean daily yield for the new process is less than that of the old procedure. Reject the null hypothesis and the mean daily yield for the new process is not less than that of the old procedure. Do not reject the null hypothesis and the mean daily yield for the new process is less than that of the old procedure. Do not reject the null hypothesis and the mean daily yield for the new process is not less than that of the old procedure.According to a survey the percent of high school graduates is 69%. One city wanted to know if the proportion of high school graduates is different from the known national proportion. The city samples 150 citizens to know if the proportion of high school graduates and 98 are graduates. (10 points) State the null and alternative hypotheses. What is the value for the t-test for the proportion? For α = .05 (two-tailed) what is the appropriate p value?