12. A random sample of n = 12 months of stock returns is taken and the...
A random sample of 100 daily stock returns was taken. The average return in the sample appeared to be 4.81%. The population standard deviation is not known, but the sample standard deviation is known to be 0.9%. a. Calculate a 95% confidence interval for the average stock return b. If the sample contained 150 stock returns, would the confidence interval found in problem 3 a) become wider? . Yes 2. No 3. The question cannot be answered with the data...
A random sample of n = 25 observations is taken from a N(µ, σ ) population. A 95% confidence interval for µ was calculated to be (42.16, 57.84). The researcher feels that this interval is too wide. You want to reduce the interval to a width at most 12 units. a) For a confidence level of 95%, calculate the smallest sample size needed. b) For a sample size fixed at n = 25, calculate the largest confidence level 100(1 −...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n 1 = 40 n 2 = 35 x 1 = 13.8 x 2 = 11.3 σ 1 = 2.5 σ 2 = 3 What is the point estimate of the difference between the two population means? (to 1 decimal) Provide a 90% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. ( , ) Provide a...
A random sample of n=12 values taken from a normally distributed population resulted in the sample values below. Use the sample information to construct a 98% confidence interval estimate for the population mean. 112 111 90 109 111 102 115 100 108 102 108 110 The 98% confidence interval is from $ to $?
Pg 417 6.47 For a hypothesis test H0: p = 0.3 Ha: p < 0.3 a random sample of size n 200 is taken and the sample proportion p = 0.21 (a) Determine whether it is appropriate to use the normal distribution to estimate the p-value. (b) If it is appropriate to use a normal distribution, complete the test for a significance level of 5% Pg 418 6.55 Home Field in Baseball 2009 There were 2430 Major League Baseball games played in 2009, and the home team won the...
A simple random sample of size N = 12 is drawn from a population that is normally distributed. The sample mean is found to be x = 59 and the sample standard deviation is found to be S = 14. Construct a 95% confidence interval about the population mean.
A simple random sample of size 64 is drawn from a normal population with a known standard deviation σ. The 95% confidence interval for the population mean μ is found to be (12, 16). The approximate population standard deviation σ is:
2. A simple random sample of size n is drawn. The sample mean I is found to be 53.1, and the sample standard deviation s is found to be 7.8 a) (3 points) Construct a 95% confidence interval for the population mean u if the sample size n is 81. b) (3 points) Construct a 95% confidence interval for the population mean u if the sample size n is 30. c) (3 points) Construct a 90% confidence interval for the...
3. Suppose that ai . ,,an are a random sample from a N( ,02) distribution. Recall that the MLE in this case is [a, σ]T = [x, V (n-1)s2/n]T and the information matrix is Consider the data s2-4.84 with n 16 (a) Use the delta-method to obtain an approximate 95% confidence interval for log(o) (b) Obtain an approximate 95% confidence interval for σ2 using the confidence interval from (a). Compare to the exact interval, [2.21,15.77], and approximate interval [0.43, 10.50...
Suppose that X . . . . . Xn is a random sample from a normal population with unknown mean μ x and unknown variance σ I. What is the form of a 95% confidence interval for μχ . Îs your interval the shortest 95% confidence interval for μχ that is avail- able? 2. What is the form of a 95% confidence interval for . Is your interval the shortest 95% confidence interval for σ,' that is avail- able? 3....