Problem #4: Suppose we know that midterm scores are normally distributed with an unknown mean . Suppose that 23students are selected at random and their average score is 66.2. Now we are interested in constructing confidenceintervals for u. We further suppose that the true population standard deviation of scores is 14.Problem #4(a):Problem #4(b):Problem #4(c):(a) Find a 96% confidence interval for u.(b) Find a 93% confidence interval for u.(c) Suppose we will take another sample and we wish to construct a 97% confidence interval with width 6. Whatsample size would be required?numbers correct to 2 decimalsnumbers correct to 2 decimals

sample size(n)=23Mean()=66.2standard deviation()=14

Answered: Problem #4: Suppose we know that…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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(4) Annual rainfall over the slopes of southern Himalayan mountains has varied from 750mm to 1250mm over the last several hundred years. If the distribution of the amount of annual rainfall has mean u = 1000mm and standard deviation o = 100mm, what is the likelihood that the average rainfall over the last ten years could have been below 800mm, in the absence of any climate change? Solve this problem by taking the following four steps one by one. Step (i). We need to compute P(X 10 < 800). where X 10 is the average over the ten years of rainfall. Can we compute this probability exactly: (a) No, the population distribution is not known. (b) Yes, since the population distribution is Poisson. (c) Yes, since the population distribution is Binomial. (d) No, because no matter what the population distribution may be, it is always impossible to find the exact distribution of X 10- (e) None of the above. (a) (b) (c) (d) (e) N/A (i- Select One) Step (ii). An approximation to the probability, P(X…
Consider the following questions about CIs. A researcher tests emotional intelligence (EI) for a random sample of children selected from a population of all students who are enrolled in a school for gifted children. The researcher wants to estimate the mean EI for the entire school. The population standard deviation, mean, for EI is not known. Let’s suppose that a researcher wants to set up a 95% CI for IQ scores using the following information: The sample mean M= 130 The sample standard deviation s = 15. The sample size N = 120. The df = N – 1 = 119 What are the upper and lower limits of the CI and the width of the 95% CI if all the other values remain the same (M = 130, s =15) but you change the value of N to 16? For N = 16, lower limit = 122.41 and upper limit=137.58 width (upper limit-lower limit = 15,17 What are the upper and lowers of CI and the width of 95% CI if all the other values remain the same but you change the value of N to 25? . For N = 25, lower limit =…
A student stated: “I fail to see why the response function needs to be constrained between 0 and 1 when the response variable is binary and has a Bernoulli distribution. The fit to 0, 1 data will take care of this problem for any response function.” Comment.
Suppose the study described in the previous question was conducted by a colleague. He tells you that based on a chi-square distribution with 2 degrees of freedom, his p-value was 0.11, and he concludes that the proportions are not the same across health status categories. Do you agree with his conclusion? Yes, by rejecting the null hypothesis, it does appear that the proportions are not the same. Yes. He should have not rejected the null hypothesis and concluded that they do not appear to be related. Yes. a p-value > 0.05 always indicates that variables are related regardless of the test conducted
(a) There are many situations in which we want to compare means from populations having standard deviations that are equal. This method applies even if the standard deviations are known to be only approximately equal. Consider a report regarding average incidence of fox rabies in two regions. For region I, n, = 14, x, = 4.75, and s, = 2.84 and for region II, n2 = 13, x2 = 3.95, and sz = 2.41. The two sample standard deviations are sufficiently close that we can assume o, = 0,. Use the method of pooled standard deviation to consider the report, testing if there is a difference in population mean average incidence of rabies at the 5% level of significance. (Round your answer to three decimal places.) It =
(g) The following question was investigated: If the standard deviation of the mean for the sampling distribution of random samples of size 64 from a large or infinite population is 5, how large must the sample size become if the standard deviation is to be reduced to 0.9. In solving this question, it was determined that n = 1975.308642. Since we cannot talk to a partial person, how many people do we need to sample? (h) Suppose you collect data and want to find P(X < some number) by using the t-distribution. What do we need to assume about the population to make sure we can use the t-distribution? (i) Suppose we want to solve the following: • Find k such that P(x2 < k) = 0.025 where df = 8. Find P(x? < 4.182) where df = 6. What R function would you use in each case to solve these questions? You do not need to actually solve, just write down the R function. An example of an R function is dbinom (this is not the one that you need).
Test the hypothesis of the following problems using the steps. 1. Ten randomly selected groceries in San Francisco has an average sales of 41 thousand dollars every 6 months with a standard deviation of 5.2 thousand dollars. Is this enough evidence to conclude that the groceries are not selling an average of 42 thousand dollars every 6 months? Test the hypothesis at a level of significance of 5%. Use a one-tailed test. 2. A certain manager wishes to find out if the proposed system of operations increases the gross sales of the products of the compared with existing system. To compare the results, six branches for each system are randomly selected for assessment. The result is as follows: Proposed system Existing system Average sales in million 42.5 32.6 Standard deviation 5.7 4.8 Number of branches 6 6 Is the proposed system significantly better than the existing system? Test at a = 0.01 and use a one-tailed test. 3. Oil wells in a large field produce an average…
25. Each of a random sample of 30 student nurses who participated in a research project was given a test designed to measure the degree of creative thinking. The standard deviation of the scores was 11. Can one conclude from these data that the population variance is less than 400? Let α = 0. 05 and assume that the population is normally distributed. (A) Yes (B) No
5. A quality control engineer found that the inner and outer diameters of their ball bearings, denoted respectively as X and Y, are random variables with E(X|Y = y) = 0.7 – 0.3y inches and Var(X|Y = y) = 0.0004y for all values of y. From his past experience he also knew that the mean and variance of the outer diameters were E(Y) = 0.7 inches, and Var(Y) squared inches. = 0.0001 %3D • (i) What are the conditional random variables, E(X|Y) and Var(X|Y)? • (ii) Find the mean of the inner diameters, E(X). • (ii) Find the variance of the inner diameters, Var(X).
You have taken a random sample of size n = 12 from a normal population that has a population mean of μ = 90 and a population standard deviation of G = 4. Your sample, which is Sample 1 in the table below, has a mean of x=89.1. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) (a) Based on Sample 1, graph the 80% and 95% confidence intervals for the population mean. Use 1.282 for the critical value for the 80% confidence interval, and use 1.960 for the critical value for the 95% confidence interval. (If necessary, consult a list of formulas.) • Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place. • For the points (and ◆), enter the population mean, μ = 90. 85.0 S1 |+H 85.0 80% confidence interval 91.0 X +|||||||| x 80% 80% 95% 95% lower upper lower upper limit limit limit limit ? 89.1 ? ? ? S2 90.7 89.2 92.2 88.4 93.0 S3 89.8 88.3 91.3 87.5 92.1 S4 91.9 90.4 S5 89.4 87.9 S6 90.8 89.3 S7 90.6…
Solve question #9 for part D only.

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