Mathematical Statistics with Applications
7th Edition
ISBN: 9781111798789
Author: Dennis O. Wackerly
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 12.3, Problem 12E
a.
To determine
Find the number of degrees of freedom that are associated with the estimator for the common variance
b.
To determine
Find the number of degrees of freedom that are associated with the estimator of
c.
To determine
Find the values of
d.
To determine
Gove the possible disadvantage to implement a matched-pair design experiment rather than independent samples.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
2. Assume that AUM body temperatures are normally distributed with o =
collected a sample with the sample mean 98° F among n =
mean body temperature in AUM.
1.5° F. We
9 this year. Let u be the
(a) Find a two-sided 95% confidence interval for u.
(b) Find an upper bounded one-sided 95% confidence interval for u.
(c) Find a lower bounded one-sided 95% confidence interval for u.
Assume that you have a sample of n1=8, with the sample mean x1=44, and a sample standard deviation of s1=5, and you have an independent sample of n2=14 from another population with a sample mean of x2=35, and the sample standard deviation s2=6. Construct a 95% confidence interval estimate of the population mean difference between m1 and m2. Assume the the two population variances are equal.
The data for a random sample of six paired observations are shown in the table.
a.
Calculatex and s
b. Express μ in terms of μ, and μ₂-
c. Form a 90% confidence interval for Hd.
d. Test the null hypothesis Ho: H = 0 against the alternative hypothesis H₂: #0. Use α=0.10.
a. Calculate the difference between each pair of observations by subtracting observation from observation 1. Find X-
(Round to two decimal places as needed.)
(-)
Pair
1
2
5
6
Population 1 Sample
(Observation 1)
5
12
11
6
3
3
Population 2 Sample
(Observation 2)
3
Q
Chapter 12 Solutions
Mathematical Statistics with Applications
Ch. 12.2 - Suppose that you wish to compare the means for two...Ch. 12.2 - Refer to Exercise 12.1. Suppose that you allocate...Ch. 12.2 - Suppose, as in Exercise 12.1, that two populations...Ch. 12.2 - Refer to Exercise 12.3. How many observations are...Ch. 12.2 - Suppose that we wish to study the effect of the...Ch. 12.2 - Refer to Exercise 12.5. Consider two methods for...Ch. 12.2 - Refer to Exercise 12.5. Why might it be advisable...Ch. 12.2 - The standard error of the estimator 1 in a simple...Ch. 12.3 - Consider the data analyzed in Examples 12.2 and...Ch. 12.3 - Two computers often are compared by running a...
Ch. 12.3 - When Y1i, for i = 1, 2,, n, and Y2i, for i = 1,...Ch. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - A plant manager, in deciding whether to purchase a...Ch. 12.3 - Muck is the rich, highly organic type of soil that...Ch. 12.3 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Complete the assignment of treatments for the...Ch. 12 - Prob. 28SECh. 12 - Prob. 29SECh. 12 - Prob. 30SECh. 12 - Prob. 31SECh. 12 - Prob. 32SECh. 12 - Prob. 33SECh. 12 - Prob. 34SECh. 12 - The earths temperature affects seed germination,...Ch. 12 - An experiment was conducted to compare mean...Ch. 12 - Prob. 37SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- The data for a random sample of six paired observations are shown in the table. a. Calculate X and s². S b. Express μ in terms of H₁ and H₂. c. Form a 90% confidence interval for μd. d. Test the null hypothesis Ho: μ = 0 against the alternative hypothesis H₂: µå ‡0. Use α = 0.10. a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1. Find Xd. Xd= (Round to two decimal places as needed.) Calculate s 2 (Round to two decimal places as needed.) b. If μ₁ and μ₂ are the means of populations 1 and 2, respectively, express μ in terms of μ₁ and µμ2. Choose the correct answer below. A. Hd=H₂ H₁ B. Hd1₁H₂ OC. Hd H₁-H₂ O D. Hd=H₂ + H₂ c. Form a 90% confidence interval for μd. (00) (Round to two decimal places as needed.) d. Test the null hypothesis Ho: μ = 0 against the alternative hypothesis H₂: Hd #0. Use α = 0.10. Calculate the test statistic. t= (Round to two decimal places as needed.) Calculate the p-value. p-value= (Round to three…arrow_forwardBob selects independent random samples from wo populations and obtains the values p1 0.700 and p2 = 0.500. He constructs the 95% confidence interval for p1 – P2 and gets: 0.200 + 1.96(0.048) = 0.200 ± 0.094. Note that 0.048 is called the estimated standard error of p1 – p2 (the ESE of the estimate). Tom wants to estimate the mean of the success ates: Pi + P2 2 (a) Calculate Tom's point estimate. (b) Given that the estimated standard er- ror of (pi + P2)/2 is 0.024, calculate the 95% confidence interval estimate of (pi + P2)/2. Hint: The answer has our usual form: Pt. est. ±1.96 × ESE of the estimate. Carl selects one random sample from a popu- ation and calculates three confidence intervals for p. His intervals are below. A C p+0.080 p±0.040 p± 0.072 Match each confidence interval to its level, with evels chosen from: 80%, 90%, 95%, 98%, and 99%. Note: Clearly, two of these levels will not be used. You do not need to explain your reasoningarrow_forward4.) A simple random sample of size n is drawn from a population that is normally distributed. Using the data, it was found to be: x-bar = 108, and s = 10. Construct a 95% confidence interval about μ if the sample size is 25. Construct a 95% confidence interval about μ if the sample size is 10. Compare your results from Parts (a) and (b). How does decreasing the sample size affect the margin of error? Construct a 90% confidence interval about μ if the sample size is 25.arrow_forward
- 4b.1A random sample of 12 pea tins from a canning factory's production is selected on a given day, and their contents are weighed. For the sample, the weight's mean and standard deviation are, respectively, 301-8 g and 1-8 g. The mean weight of peas in tins produced by the factory on the relevant day should have 99% confidence limits.The mean and standard deviation of the contents for this sample are 302-1 gm and 1-6 gm, respectively, the day after another random sample of 12 tins is obtained. AssumingA 95% confidence interval demonstrates that the variances of the weights are the same on the two days interval includes 0 for the mean weight difference between the two days.NextNow suppose that the samples from both days come from the same population. Using both samples, calculate a 99% confidence interval for the mean weight of tins in that population.arrow_forward2. Two detergents were tested for their ability to remove stains. The first one was suc- cessful on 63 out of 91 trials and the second one was successful on 42 out of 79 trials. Construct approximated 95% one-sided confidence intervals for the difference pi – P2 where the successful rates are pi and p2, respectively.arrow_forwardSuppose the following table illustrates the ages for a number of participants projected to enroll into a clinical trial looking at early onset of dementia. Patient Age A 64 B 57 C 58 D 53 E 71 F 54 G 63 A) Assuming that these participants can be considered to be normally distributed, and that they come from a population with a σ=4.3 years. Calculate a 90% confidence interval for the mean age of the population for which they represent.arrow_forward
- Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C.I) = the width of the confidence interval for the average value y for a given value of x, and Width (P.I) = the width of the prediction interval for a single value y for a given value of x. Which of the following statements is true? Width (C.I) = 0.5 Width (P.I) Width (C.I) = Width (P.I) Width (C.I) > Width (P.I) Width (C.I) < Width (P.I)arrow_forwarda. What are the sample estimates of β0,β1,and β2? b. What is the least squares prediction equation? c. FindSSE,MSE,and standard deviation . Interpret the standard deviation in the context of the problem. d. Test H0: β1=0 against Ha: β1≠0.Use α=0.01. e. Use a 95% confidence interval to estimate β2. f. Find R2 and R^2_a and interpret these values. g. Find the test statistic for testing H0: β1=β2=0. h. Find the observed significance level of the test in part g.interpret the result.arrow_forwarddo for b, c, and d also remember to find he 99% confidence interval tooarrow_forward
- 4 and 5arrow_forwardGiven are five observations for two variables, x and y. 3 7 8 12 18 8 18 7 27 22 Develop the 90% confidence and prediction intervals when a = 9. (to 4 decimals) t-value (to 3 decimals) (to 4 decimals) Spred (to 4 decimals) Confidence Interval for æ = 9 ) (to 2 decimals) Prediction Interval for æ = 9 ) (to 2 decimals) The two intervals are different because there is more variability associated with predicting- Select your answer - v value than there is - Select your answer value.arrow_forwarda) Determine 99% confidence limits for beta(symbol couldn't write) (the slope of the regression line) and alpha (the intercept of the regression line). b) 34. Determine 99% prediction limits for Y when X = 41.7 and 95% prediction limits for Y when X = 61.5. c) draw a scatter plot.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License