**Find the value of the test statistic.**\( T^+ = \) [Input box for answer]**Find the \( p \)-value. (Round your answer to four decimal places.)**\( p \)-value = [Input box for answer]*Note: Be sure to calculate the test statistic and use appropriate statistical methods to determine the \( p \)-value, rounding correctly to four decimal places for accurate results.* In this exercise involving paired differences, consider that it is reasonable to assume the populations being compared have approximately the same shape and that the distribution of paired differences is approximately symmetric.Two fuel additives are tested to determine their effect on miles per gallon for passenger cars. Suppose test results for 12 cars follow; each car was tested with both fuel additives.| Car | Additive 1 | Additive 2 ||-----|------------|------------|| 1 | 19.12 | 17.05 || 2 | 24.56 | 20.77 || 3 | 23.03 | 23.57 || 4 | 18.15 | 17.06 || 5 | 22.23 | 20.22 || 6 | 23.77 | 24.80 || 7 | 15.16 | 16.20 || 8 | 19.55 | 14.98 || 9 | 21.87 | 20.03 || 10 | 23.23 | 21.15 || 11 | 23.21 | 23.78 || 12 | 24.02 | 22.70 |This table shows the miles per gallon for each car when using two different fuel additives. The data can be used to analyze the performance differences between the two additives for each vehicle.

Given information: Additive Car 1 2 1 19.12 17.05 2 24.56 20.77 3 23.03 23.57 4 18.15…

Answered: In this exercise involving paired…

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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In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance. City: 16.7 17.2 16.4 14.9 13.7 15.8 17.3 16.5 16.6 15.8 15.7 15.8 16.7 Highway: 20.0 21.2 18.9 19.2 19.8 18.0 17.8 19.2 19.6 21.7 20.0 19.1 19.3 Calculate the mean, median, and mode for City and Highway gasoline consumption (to 1 decimal). City Highway Mean Median Mode The data are bimodal:   and
Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 15.8 17.3 14.4 19.6 20.0 Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1,540.45; Σxy = 272 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = +  x (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. (c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is…
Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 13.8 19.3 14.4 19.6 20.0 Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1554.45; Σxy = 274b) Find the equation of the least-squares line. (Round your answers to two decimal places.) ŷ = +  x (c) Find r. Find the coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = d) Test the claim that the population correlation coefficient is positive at the 1% level of significance. (Round your test statistic to three decimal places.) t =
Below are four bivariate data sets and their scatter plots. (Note that all of the scatter plots are displayed with the same scale.) Each data set is made up of sample values drawn from a population. A. For which data set is the sample correlation coefficient r equal to −1? B. For which data set is the sample correlation coefficient r closest to 0?
Which of the following research scenarios uses a two samples independent-measures t test? a. Examine the difference in self-esteem between student athletes and non-athletes. b. Evaluate the effectiveness of a pain reliever by measuring how much pain is reduced after taking the medication in a single group of people who rated pain, then took the drug and rated pain a second time. c. Test the effectiveness of a cholesterol medication by comparing cholesterol levels before and after the medication is administered to a single group. d. Calculating the z score for the highest X in the data set.
Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 15.8 17.3 14.4 19.6 20.0 Σx = 15; Σy = 87.1; Σx2 = 55; Σy2 = 1,540.45; Σxy = 272 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.) x = y = b = ŷ = + x
Suppose we have the following paired observations of variables X and Y: X Y 8 0 4 10 12 20 Draw the scatter plot comparing X and Y. Calculate the values of the sample covariance and sample correlation between X and Y. Using this information, how would you characterize the relationship between X and Y ?
a survey is conducted to compare the proportions of men and women whoaccess their bank statements online. Denoting the population propotions by Pm and Pw, a two-proportion z-test is carried out to test Ho: pm = pw against Ha: pm > pw. The values of the test statistic is found to be z = 0.784, and the p-value for the test is found to be 0.216. Which of the following is the correct interpretation of the p-value? a) given that ha is true, the probability of getting a value of z at least as large as 0.784 is 0.216. b) given the results of the survey, the probability that Pm > Pw is 0.216. c) given the results of the survey, the probability that Pm = Pw is 0.216. d) none of the above
Use the data and table below to test the indicated claim about the means of two paired populations (matched pairs). Assume that the two samples are each simple random samples selected from normally distributed populations. Make sure you identify all values. The table below shows the blood glucose of 20 students before breakfast and two hours after breakfast, using a specific insulin dosing formula to cover carbohydrates. Is there compelling statistical evidence that the specific insulin dosing formula is effective in reducing blood glucose levels? Use a significance level of 0.05. We have the differences (gain or loss), but we still need to compute the mean, standard deviation, and know the sample size for the differences (use Excel or Sheets for this computation). Once those are found, we can apply methods that are used for a 1 sample t-test. Student Before Meal After Meal Difference 1 161 114 -47 2 196 88 -108 3 132 80 -52 4 175 96 -79 5 169 112 -57 6 138 137…
A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen, resulting in the accompanying data. 1.16 5.09 0.97 1.59 4.60 0.32 0.55 1.45 0.16 4.47 1.20 3.50 5.02 4.67 5.22 2.69 3.97 3.17 3.03 2.21 0.69 4.47 3.31 1.17 0.77 1.17 1.57 2.62 1.66 2.05 The values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.484, 1.612, and 0.294, respectively. Does this data suggest that the true average percentage of organic matter in such soil is something other than 3%? Carry out a test of the appropriate hypotheses at significance level 0.10. [Note: A normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.] State the appropriate hypotheses. ⒸH₁: μ = 3 H₂:μ # 3 OH:μ #3 Ha: μ 3 t = P-value = Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal…
The accompanying table shows the ages (in years) of 11 children and the numbers of words in their vocabulary. 1. Calculate the sample correlation coefficient r. r = ____. 2. Determine the critical value.

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