Exercise 15. For the following four cases, perform statistical tests with significance level a = 5%,testing the hypothesis Ho: μ = 0 against the alternative H₁: 0. Show how you perform eachtest and state the outcome.a) We have observed 100 independent, normally distributed values with known variance o² = 1.The average of the observed values is -0.18.b) We have observed 10 independent samples of a normal distribution with known varianceo² = 4: The observed values are 0.595, 3.923, 0.12, 1.078, 0.578, 1.575, 2.26, -0.031, 1.733,and 1.135.c) We have observed 10 independent samples from a normal distribution. The sample mean is* = -1.405, the exact variance is unknown but the sample variance is s2 = 1.456.

Introduction: A z-test is a type of statistical hypothesis test that is used to determine whether…

Answered: Exercise 15. For the following four…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

The yield per tract in a certain region of farmland is known to have a populationstandard deviation of 13 bushels. Using the old seed variety, the population mean yield μwas 39 bushels. A farmer tests a new seed variety on a random sample of 36 tracts, andfinds a sample mean yield of 45.2 bushels. Is the population mean yield using the newseed variety different from 39? Use α= 0.10.a. State the null hypothesis . __________________State the alternative hypothesis.____________________b. Find the test statistic. _____ c. Find the P-value for the test. _____________
You are interested in testing whether the average age of household heads is higher in the suburbs than in inner city neighbourhoods. A survey is conducted, and the following results are obtained. In the suburbs, the household heads of the 45 households surveyed had a mean age of 44 with a standard deviation of 15. In the inner city, the mean age of the 40 household heads surveyed was 38 with a standard deviation of 13. Assuming that the populations from which these samples were drawn have equal variances, can you conclude that the difference between the two means is significant at the 95% level of confidence? (a) Write in words and symbols the null and research hypotheses. (b) Assuming the variances of the populations are equal, calculate the value of the Pooled Variance Estimate (PVE). (c) Calculate the value of the standard error for the difference between the two means.
Two samples were drawn independently from two normal populations. Sample 1: 11.6, 11.35, 10.1, 10.85, 10.35, 10.6, and 11.1.Sample 2: 5.85, 8.85, 9.85, 11.85 and 7.85.Test to determine whether the means of the two population differs (use α=0.05).
A researcher wonders whether the recession has changed variability in family size in his city. Before the recession, the mean was 3.7 and the standard deviation was 1.76. The researcher randomly selects 41 families from a population that is normally distributed. His sample has a mean of 3.1 and a standard deviation of 1.45. Test the claim that the standard deviation in size has changed at the αα=.05 significance level.
The average score on a statistics test was 2.52 with a standard deviation of 0.75. The teacher suspects that the exam was very difficult; Based on the above, he wants to adjust the scores so that the mean is 3.58 and the standard deviation is 0.25. Compute the values a and b such that the fit of type aX+b provide the desired mean and variance? Calculate: a=?b=?
A study was conducted to determine if the performance of a certain type of surgery on young horses had any effect on certain kinds of blood cell types in the animal. Fluid samples were taken from each of six foals an hour after the operation. Suppose that the data on WBC leukocytes follow the normal distribution. One sample Chi-squared test for variancedata: wbcX-squared = 3.5321, df = 5, p-value = 0.3815alternaative hypothesis: true variance is less than 4 Question: Is there evidence to say that the variance of WBC leukocytes is less than 4? State the conclusion based from the results of the test. Choices:- There is no sufficient evidence that the variance of WBC leukocytes is less than 4.- There is a sufficient evidence that the variance of WBC leukocytes is less than 4.
Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 32 PlayStation users had an average age of 33.7 years while a random sample of 36 Xbox users had an average age of 35.6 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.7 and 3.5 years, respectively. Sony would like to set alpha is 0.10. The critical value for this hypothesis test would be
In a class of twenty-five 15-year old girls the average height is M = 62.60 inches. The national average for girls at this age is reported as follows: µ = 63.80 inches with a standard deviation, s = 2.66 inches. 1. What is the effect size Cohen’s d and what does it tell us about the effect? 2. Compute the z-statistic.
For a repeated-measures study comparing two treatment conditions, a researcher obtains a sample of n = 10 difference scores with a mean of MD = 6 and a variance of s2 = 90. What is the value for the repeated-measures t statistic for these data? Select one: a. 7 b. 6 c. 2 d. 15
You are conducting a study to see if the accuracy rate for fingerprint identification is significantly different from 0.51. Thus you are performing a two-tailed test. Your sample data produce the test statistic - 2.153. Find the p-value accurate to Z = - 4 decimal places. p-value
You have data drawn from a normal distribution with a known variance of 16. You set up the following NHST: • Ho: data follows a N(2, 4²) • HÃ: data follows a N(µ, 4²) where µ ‡ 2. Test statistic: standardized sample mean z. Significance level set to a = .05. You then collected n = 16 data points with sample mean 1.5. (a) Find the rejection region. Draw a graph indicating the null distribution and the rejection region. (b) Find the z-value and add it to your picture in part (a). (c) Find the p-value for this data and decide whether or not to reject Ho in favor of HA.
Data on the weights (Ib) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Diet Regular H2 26 26 0.79911 Ib 0.81326 Ib S 0.00445 Ib 0.00759 Ib ..... a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? A. Ho: Hy =H2 H1: 41> H2 B. Ho: H1 = H2 H1: 41

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS