Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 11.8, Problem 57E
a.
To determine
Obtain the term in the T statistic that determines whether the value of t is negative or positive.
b.
To determine
Obtain the quantities that determine the size of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
11.25 Refer to Exercise 11.24. Fit a regression model relating yield to the absolute deviationfrom the ideal planting date, that is, x 5 |D|.a. Compute the estimated linear regression model ^ y 5 ^b0 1 ^b1x.b. Estimate s2e.c. Estimate the standard error of b ^ 1.d. Place a 95% confidence interval on b1.e. Test the hypothesis that there is a linear relationship between yield per acre andabsolute deviation from the ideal planting date. Use a 5 .05.
Consider an estimated linear regression model with a response Y and 4 predictors X1, X2, X3, X4. For a random sample of 25 observations on the response and the 4 predictors, the following estimates are obtained using Excel.
Regression Statistics
Multiple R
0.859825564
Standard Error
127.606
What is the adjusted R-square of the fitted model?
What type of statistical test are you conducting if h1 states that the parameter is greater than the value claimed in h0?
a) left-tailed
b) right-tailed
c) two-tailed
d) dove-tailed
Chapter 11 Solutions
Mathematical Statistics with Applications
Ch. 11.3 - If 0 and 1 are the least-squares estimates for the...Ch. 11.3 - Prob. 2ECh. 11.3 - Fit a straight line to the five data points in the...Ch. 11.3 - Auditors are often required to compare the audited...Ch. 11.3 - Prob. 5ECh. 11.3 - Applet Exercise Refer to Exercises 11.2 and 11.5....Ch. 11.3 - Prob. 7ECh. 11.3 - Laboratory experiments designed to measure LC50...Ch. 11.3 - Prob. 9ECh. 11.3 - Suppose that we have postulated the model...
Ch. 11.3 - Some data obtained by C.E. Marcellari on the...Ch. 11.3 - Processors usually preserve cucumbers by...Ch. 11.3 - J. H. Matis and T. E. Wehrly report the following...Ch. 11.4 - a Derive the following identity:...Ch. 11.4 - An experiment was conducted to observe the effect...Ch. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - A study was conducted to determine the effects of...Ch. 11.4 - Suppose that Y1, Y2,,Yn are independent normal...Ch. 11.4 - Under the assumptions of Exercise 11.20, find...Ch. 11.4 - Prob. 22ECh. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Do the data in Exercise 11.19 present sufficient...Ch. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Let Y1, Y2, . . . , Yn be as given in Exercise...Ch. 11.5 - Prob. 30ECh. 11.5 - Using a chemical procedure called differential...Ch. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - Prob. 34ECh. 11.6 - For the simple linear regression model Y = 0 + 1x...Ch. 11.6 - Prob. 36ECh. 11.6 - Using the model fit to the data of Exercise 11.8,...Ch. 11.6 - Refer to Exercise 11.3. Find a 90% confidence...Ch. 11.6 - Refer to Exercise 11.16. Find a 95% confidence...Ch. 11.6 - Refer to Exercise 11.14. Find a 90% confidence...Ch. 11.6 - Prob. 41ECh. 11.7 - Suppose that the model Y=0+1+ is fit to the n data...Ch. 11.7 - Prob. 43ECh. 11.7 - Prob. 44ECh. 11.7 - Prob. 45ECh. 11.7 - Refer to Exercise 11.16. Find a 95% prediction...Ch. 11.7 - Refer to Exercise 11.14. Find a 95% prediction...Ch. 11.8 - The accompanying table gives the peak power load...Ch. 11.8 - Prob. 49ECh. 11.8 - Prob. 50ECh. 11.8 - Prob. 51ECh. 11.8 - Prob. 52ECh. 11.8 - Prob. 54ECh. 11.8 - Prob. 55ECh. 11.8 - Prob. 57ECh. 11.8 - Prob. 58ECh. 11.8 - Prob. 59ECh. 11.8 - Prob. 60ECh. 11.9 - Refer to Example 11.10. Find a 90% prediction...Ch. 11.9 - Prob. 62ECh. 11.9 - Prob. 63ECh. 11.9 - Prob. 64ECh. 11.9 - Prob. 65ECh. 11.10 - Refer to Exercise 11.3. Fit the model suggested...Ch. 11.10 - Prob. 67ECh. 11.10 - Fit the quadratic model Y=0+1x+2x2+ to the data...Ch. 11.10 - The manufacturer of Lexus automobiles has steadily...Ch. 11.10 - a Calculate SSE and S2 for Exercise 11.4. Use the...Ch. 11.12 - Consider the general linear model...Ch. 11.12 - Prob. 72ECh. 11.12 - Prob. 73ECh. 11.12 - An experiment was conducted to investigate the...Ch. 11.12 - Prob. 75ECh. 11.12 - The results that follow were obtained from an...Ch. 11.13 - Prob. 77ECh. 11.13 - Prob. 78ECh. 11.13 - Prob. 79ECh. 11.14 - Prob. 80ECh. 11.14 - Prob. 81ECh. 11.14 - Prob. 82ECh. 11.14 - Prob. 83ECh. 11.14 - Prob. 84ECh. 11.14 - Prob. 85ECh. 11.14 - Prob. 86ECh. 11.14 - Prob. 87ECh. 11.14 - Prob. 88ECh. 11.14 - Refer to the three models given in Exercise 11.88....Ch. 11.14 - Prob. 90ECh. 11.14 - Prob. 91ECh. 11.14 - Prob. 92ECh. 11.14 - Prob. 93ECh. 11.14 - Prob. 94ECh. 11 - At temperatures approaching absolute zero (273C),...Ch. 11 - A study was conducted to determine whether a...Ch. 11 - Prob. 97SECh. 11 - Prob. 98SECh. 11 - Prob. 99SECh. 11 - Prob. 100SECh. 11 - Prob. 102SECh. 11 - Prob. 103SECh. 11 - An experiment was conducted to determine the...Ch. 11 - Prob. 105SECh. 11 - Prob. 106SECh. 11 - Prob. 107SE
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
- You have obtained a sub-sample of 1744 individuals from the Current Population Survey (CPS) and are interested in the relationship between weekly earnings and age. The regression, using heteroskedasticity-robust standard errors, yielded the following result: = 239.16 + 3.75× Age, R2 = 0.15, SER = 287.21., where Earn and Age are measured in dollars and years respectively. Interpret the intercept? Interpret the slope coefficient b) Is the effect of age on earnings large? The average age in this sample is 37.5 years. What is annual income in the sample? (e) Interpret the measures of fit.arrow_forwardStock y has a beta of 1.2 and an expected return of 11.5. Stock z has a beta of .80 and an expected return of 8.5 percentarrow_forwardConsider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. Using the 68-95-99.7 rule, between what two values would approximately 95% of the observed responses, y, fall when x = 7?arrow_forward
- A scientist studying local lakes claims that there is a linear relationship between a lake’s level of mercury and the lake’s depth. The scientist collected data to test the claim at a significance level of α=0.01. The following hypotheses were tested. H0:β1=0Ha:β1≠0 The test yielded a t-value of 2.7 and a p-value of 0.012. Which of the following is a correct conclusion about the scientist’s claim? The null hypothesis is rejected since 0.012>0.01. There is sufficient evidence to suggest that there is a linear relationship between a lake’s level of mercury and the lake’s depth. A The null hypothesis is not rejected since 0.012>0.01. There is sufficient evidence to suggest that there is a linear relationship between a lake’s level of mercury and the lake’s depth. B The null hypothesis is rejected since 0.012>0.01. There is not sufficient evidence to suggest that there is a linear relationship between a lake’s level of mercury and the lake’s depth.…arrow_forwardA snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.33. A dietician is asked to test this claim and finds that a random sample of 24 servings has a variance of 1.37. At α=0.01, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below. (a) Write the claim mathematically and identify H0 and Ha. A. H0: σ2≤1.33 (Claim) Ha: σ2>1.33 B. H0: σ2≠1.33 Ha: σ2=1.33 (Claim) C. H0: σ2≥1.33 Ha: σ2<1.33 (Claim) D. H0: σ2=1.33 (Claim) Ha: σ2≠1.33 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is(are) enter your response here. (Round to two decimal places as needed. Use a comma to separate answers as needed.) Choose the correct statement below and fill in the corresponding answer boxes. A. The…arrow_forwardIn a simple linear regression based on 30 observations, it is found that b1 = 3.57 and se(b1) = 1.36. Consider the hypotheses:H0: β1 = 0 and HA: β1 ≠ 0.a. Calculate the value of the test statistic. (Round your answer to 3 decimal places.) b. Find the p-value. [Hint: The test statistic has a t-distribution with df = 30 – 2. Refer to Chapter 9 of the formula sheet to get the appropriate p-value.] p-value < 0.01 0.01 p-value < 0.02 p-value 0.10 0.05 p-value < 0.10 0.02 p-value < 0.05 c. At the 5% significance level, what is the conclusion? Is the explanatory variable statistically significant? Reject H0; the explanatory variable is significant. Reject H0; the explanatory variable is not significant. Do not reject H0; the explanatory variable is significant. Do not reject H0; the explanatory variable is not significant.arrow_forward
- The results for the regression are as follows Coefficients Standard Error T stat Intercept 14.63 0.5226 27.995 financial crisis 13.71 1.0610 12.922 COVID-19 crisis 15.71 1.6643 9.439 transition 5.40 1.1835 4.563 In estimating the regression, you are also concerned that the t-statistics may be inflated because of the presence of conditional heteroscedasticity. You conduct a regression of the squared residuals against the dummy variables X1, X2, and X3 and find that for the squared residuals regression: Multiple R 0.4145 R Square 0.1718 Adjusted R Square 0.1600 SEE 92.3760 Conduct a test at the level to see if conditional heteroskedasticity is present In view of your answer for a), what needs to be done?arrow_forwardA researcher conducts a hypothesis test using a sample of n = 20 with M = 34 and s 2 = 36 from an unknown population. What is the df value for the t statistic?arrow_forwardA researcher conducts a hypothesis test using a sample of n=20 with M =34 and s^2=36 from an unknown population.What is the df value for the t statistic?arrow_forward
- bservations on years of education and hourly wages are sampled for 32 individuals and the regression wage=f(education) yields estimates β^1=12.5 and β^2=3.7. At α=0.01 what is the critical value for a left-tailed test of β2? A. 2.750 B. 5% C. none of the answers provided are correct because a left-tailed t-test has a negative critical value. D. 1.697 E. 2.457arrow_forwardA random sample of 50 students was asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 0.83 and the sample kurtosis was 3.98. Test at the 10% level the null hypothesis that the population dis- tribution of amounts spent is normal.arrow_forwardThe Road Department is trying to see whether they should buy road treatments ( in tons) for storms based on the number of inches of snow for each recorded. Use Pearson r at alpha- 0.05 to test the hypothesis. ILLUSTRATE THE NORMAL CURVE inches in snow 1.5 1.7 3.7 2.8 4.6 2.4 3.1 2.9 3.6 4.2 3.1 number of tons 805 905 1235 1000 1302 998 1102 1305 1456 1600 1005arrow_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