To study the water PH level, two independent lakes were selected for sampling. In a duration ofone year, 12 samples (one in each month) are selected from each lake. The PH mean and standarddeviation of lake 1 sample were found to be 6.5 and 0.2, while the PH mean and standard deviationof lake 2 sample were found to be 7.2 and 0.1.(a) Find a 90% confidence interval for µ1 – µ2 (i.e., the difference between the population meansfor the two lakes) assuming that the populations are approximately normally distributed with equalvariances.(b) You decide to change the above significance level from 0.1 to 0.05. Everything else is keptsimilar to above. Explain how your calculated confidence interval will change, and why? (i.e., willit become wider or narrower). (No need to calculate the new confidence interval) (- :

We associate with the interval estimate is called a confidence interval. This probability indicates…

Answered: one year, 12 samples (one in each…

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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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.
Develop a 95% confidence interval for the population slope if the followingregression information are given: b1= 41.7, p-value = 0.02, and n = 35.
Suppose we have two normal populations denoted A and B, and we want to compare their population variances by estimating the ratio: variance of population B divided by variance of population A. We have an independent random sample of size 15 from population A and an independent random sample of size 9 from population B. The sample variance for population B turns out to be 30 percent larger than that for population A. What is the 99 percent confidence interval for the ratio: population variance of population B divided by population variance of population A? Use stattrek.org for finding the needed critical values.
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)?
Given two independent random samples with the following results: n1=12x‾1=73s1=27n1=12x‾1=73s1=27 n2=12x‾2=102s2=22n2=12x‾2=102s2=22 Use this data to find the 95%95% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval.
A two-way ANOVA experiment with interaction was conducted. Factor A had three levels (columns), factor B had five levels (rows), and six observations were obtained for each combination. Assume normality in the underlying populations. The results include the following sum of squares terms: SST=1542 SSA= 1042 SSB = 358 SSAB = 39 a. Construct an ANOVA table. (Round "MS" to 4 decimal places and "F" to 3 decimal places.) ANOVA Source of Variation Rows Columns Interaction Error Total SS 0 df Answer is not complete. 0 MS F p- value 0.000 0.000 0.002
The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected astronomical objects. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 90% confidence level with a redshift of 0.0126. Redshift Distance 0.0238 0.31 a. Find the explained variation. 0.0543 0.74 (Round to six decimal places as needed.) b. Find the unexplained variation. (Round to six decimal places as needed.) c. Find the indicated prediction interval. 0.0722 1.02 billion light-years
2. We performed a linear regression using 25 observations. From the regression output we find that bo = 5.7, bị = 12.9, x = 11.4, Sz = 3.2 and MSE = 12.25. a. From the least squares line, what is the predicted response when x* = 10.65? y = b. What is the 95% confidence interval for the mean response when x* = 10.65? c. What is the 95% prediction interval for an individual response when x* = 10.65? d. Which interval is wider? The confidence interval or the prediction interval? O a. Confidence Interval b. Prediction Interval
Find a 95% confidence interval that contains the population variance if a sample of 41 generates a sample variance of 25. Show the formula used and the quantities used and obtained from the table.
Question 9 Two independent samples are selected from two populations with means µg and u2, respectively. Suppose a 99% confidence interval for u1 - H2 is (-1.65, 21.65), a 95% confidence interval is (0.2, 19.8), and a 90% confidence interval is (1.775, 18.225). In testing Ho : H1 - H2 = 0 versus H1: H1 - H2 0, the p-value is between 0.20 and 1.00 between 0.10 and 0.15 between 0.05 and 0.10 between 0.01 and 0.05. between 0.15 and 0.20

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