Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
3rd Edition
ISBN: 9781259969454
Author: William Navidi Prof.; Barry Monk Professor
Publisher: McGraw-Hill Education
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Chapter 13, Problem 4CQ
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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)
True or False: Explain
Suppose that OLS is unbiased for the following bivariate model: Y = B0 +B1X +u and suppose that the true slope coefficient B1 = 7. If you use the standard t-statistic to test the null hypothesis that the slope coefficient is equal to 0, the probability that you will reject the null hypothesis will increase if you reduce your sample size.
a) Compute the least-squares line for predicting y from 1/x. Round the answers to three decimal places.
b) Using the better fitting line, find a 95% confidence interval for the mean value of y when x = 5.0. Round the answers to three decimal places.
The 95% confidence interval for the mean value of y when x = 5.0 is?
Chapter 13 Solutions
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
Ch. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - In Exercises 9 and 10, determine whether the...Ch. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16E
Ch. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Prob. 26aECh. 13.1 - Calculator display: The following TI-84 Plus...Ch. 13.1 - Prob. 28aECh. 13.1 - Prob. 29ECh. 13.1 - Prob. 30ECh. 13.1 - Confidence interval for the conditional mean: In...Ch. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Dry up: Use the data in Exercise 26 in Section...Ch. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - In Exercises 9 and 10, determine whether the...Ch. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - For the following data set: Construct the multiple...Ch. 13.3 - Engine emissions: In a laboratory test of a new...Ch. 13.3 - Prob. 16ECh. 13.3 - Prob. 17ECh. 13.3 - Prob. 18ECh. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13 - A confidence interval for 1 is to be constructed...Ch. 13 - A confidence interval for a mean response and a...Ch. 13 - Prob. 3CQCh. 13 - Prob. 4CQCh. 13 - Prob. 5CQCh. 13 - Prob. 6CQCh. 13 - Construct a 95% confidence interval for 1.Ch. 13 - Prob. 8CQCh. 13 - Prob. 9CQCh. 13 - Prob. 10CQCh. 13 - Prob. 11CQCh. 13 - Prob. 12CQCh. 13 - Prob. 13CQCh. 13 - Prob. 14CQCh. 13 - Prob. 15CQCh. 13 - Prob. 1RECh. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Air pollution: Following are measurements of...Ch. 13 - Icy lakes: Following are data on maximum ice...Ch. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Prob. 1WAICh. 13 - Prob. 2WAICh. 13 - Prob. 1CSCh. 13 - Prob. 2CSCh. 13 - Prob. 3CSCh. 13 - Prob. 4CSCh. 13 - Prob. 5CSCh. 13 - Prob. 6CSCh. 13 - Prob. 7CS
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- If an independent variable's null hypothesis is rejected, it should remain in the model. True Falsearrow_forwardA least-squares regression line for a set of data with dependent variable y and independent variable x produces a 95% confidence interval [-0.5,1.8] on the regression slope (beta). We can conclude that: the predicted value of y for a given x will lie in the range [-0.5x,1.8x] 95% of the time the regression slope must be zero O beta will fall inside the range [-0.5,1.8] 95% of the time The data show no evidence of a linear relation between x and y O none of thesearrow_forwardIn this section, we used the statistic b1 as a basis for conducting a hypothesis test to decide whether a regression equation is useful for prediction. Identify two other statistics that can be used as a basis for such a test.arrow_forward
- True of False. If a 90% confidence interval estimate for the population mean score of all Physics students taking the exam is (70, 75), then around 90% of these students will have scores ranging from 70 to 75. Is this sampling method Related or Independent? A researcher wants to find out the efficacy of a certain detergent brand in removing stains. To do this, she got a large piece of cloth and purposely stained the whole area. She then cut the cloth into two halves and the first half is treated with the detergent and the other is submerged in water. The amount of stain removed is measured after 3 hours.arrow_forwardSuppose we have two SRSS from two distinct populations and the samples are independent. We measure the same variable for both samples. Suppose both populations of the values of these variables are normally distributed but the means and standard deviations are unknown. For purposes of comparing the two means, we use (a) Two-sample t procedures (b) Matched pairs t procedures (c) z procedures (d) The least-squares regression line (e) None of the above. The answer isarrow_forward3)A paper reported that a simple linear regression model was built based on 24 samples. The 95% confidence interval for the slope was (3.3, 9.1). a)What is thet statistic for the slope? b)What is the 99% confidence interval for the slope? c)Is the model significant at 1% significance? d)What is the R2 for the model?arrow_forward
- Probability Questionarrow_forward5) What is true about a regression using data from a randomized controlled trial? a) The independent variable is exogenous because it was determined randomly. b) The line of best fit does not minimize the sum of squared residuals. c) It eliminates all error due to unmeasured variables. d) The estimated slope is significant no matter how many observations are in the sample. e) The slope of the line of best fit must be equal to the true relationship.arrow_forwardSuppose you run a simple regresson model and you obtain estimator βˆ 1 (β1 is the population parameter). Does it make sense to compute a confidence interval for βˆ 1? If β1 represents the return to education seen in examples in class, how would you interpret a 95% confidence interval?arrow_forward
- ONLY PART 4!! The following table(see attachment) compares U.S. population (millions) with U.S. per-capita consumption of bottled water (gallons). Answer the following questions. 1. Determine the least-squares regression line and the value of r.2. Compute a 95% confidence interval for mean of the per capita consumption of bottled water, given the U.S. population is 320 million.3. Compute a 95% prediction interval for an individual observation of per capita consumption of bottled water, given the U.S. population is 320 million.4. Compare the confidence interval and prediction interval. Which one is wider? And why? You may use the critical values as below: t(0.025,3)= 3.182446, t(0.025,4)=2.776445.arrow_forwardA sample of size 10 has a sample mean of 1000 and a sample variance of 100. Then a 90% Confidence Interval for u isarrow_forwardA random sample of 15 college soccer players were selected to investigate the relationship between heart rate and maximal oxygen uptake. The heart rate and maximal oxygen uptake were recorded for each player during a training session. A regression analysis of the data was conducted, where heart rate is the explanatory variable and maximal oxygen uptake is the response variable. If a 95 percent confidence interval is constructed for the slope of the population regression line, which of the following is a condition that must be checked? A)The true relationship between heart rate and maximal oxygen uptake is linear. B)The correlation between heart rate and maximal oxygen uptake is not equal to zero. C)The confidence interval is not biased. D).The point (x_,y_) falls on the regression line. The X and Y have a line on top. E)The slope is not equal to zero.arrow_forward
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