A nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless examine the relationship between scores on such tests and performance in college.We have chosen a random sample of 99 students just finishing their first year of college, and for each student we've recorded her score on one such standardized test and her grade point average for her first year in college. The sample correlation coefficient $ r $ for our data is approximately 0.14. Based on these sample results, test for a significant linear relationship between the two variables score on this standardized test and first-year college grade point average by doing a hypothesis test regarding the population correlation coefficient $ \rho $. (Assume that the two variables have a bivariate normal distribution.) Use the 0.10 level of significance, and perform a two-tailed test. Then complete the parts below.(If necessary, consult a list of formulas.)**(a)** State the null hypothesis $ H_0 $ and the alternative hypothesis $ H_1 $.$ H_0 : $ □$ H_1 : $ □**(b)** Determine the type of test statistic to use.\[ \text{(Choose one)} \]**(c)** Find the value of the test statistic. (Round to three or more decimal places.)\[ \text{□} \]**(d)** Find the $ p $-value. (Round to three or more decimal places.)\[ \text{□} \]**(e)** Based on the sample results, can we conclude (using the 0.10 level) that there is a significant linear relationship between score on the standardized test and first-year college grade point average?\[ \text{Yes} \] \[ \text{No} \]The side panel includes various statistical symbols and notations for selection in formulating hypotheses, including symbols for mean ($ \mu $), correlation ($ \rho $), and other statistical parameters.

The independent variable is standardized test score. The dependent variable is first-year college…

Answered: A nationwide standardized test taken by…

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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Data from a certain city shows that individuals with more pets tend to have lower blood pressure (BP). From this information alone, we can say that pet ownership and BP are negatively (inversely) correlated. This may or may not be a causal relationship. pet ownership and BP are not related. pet ownership causes BP to be lower. pet ownership and BP are positively related. This may or may not be a causal relationship. 000
Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities? 358 484 Lemon Imports Crash Fatality Rate 228 531 266 15.7 15.8 15.5 15.2 14.8 What are the null and alternative hypotheses? O B. Ho: p=0 O A. Ho: p#0 H: p=0 H;:p0 H,:p#0 Construct a scatterplot. Choose the correct graph below. O A. OB. Oc. OD. Ay 17- Ay 17- Ay 17- Ay 17- Q 16- 16- 16- 16- 15- 15- 15- 15- 14+ 14- -> 14+ -> 14+ -> 200 400 600 200 400 600 200 400 600 200 400 600
Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights Correlation Results of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? Use a significance level of a = 0.05. Correlation coeff, r: 0.969467 Critical r: +0.2680855 P-value (two tailed): 0.000 ..... Determine the null and alternative hypotheses. Ho: P (Type integers or decimals. Do not round.) Identify the correlation coefficient, r. r= (Round to three decimal places as needed.) Identify the critical value(s). (Round to three decimal places as needed.) A. There are two critical values at r= + В. There is one critical value at r= Is there sufficient evidence to support the…
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Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a =0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities? 228 Lemon Imports Crash Fatality Rate 266 358 484 531 15.8 15.7 15.5 15.2 14.8 O C. Ho: p=0 YD. Ho: p=0 H,:p>0 H1: p#0 Construct a scatterplot. Choose the correct graph below. O A. В. Oc. C. OD. Ay 17- Ay 174 Ay 17- Ay 17- 16- 16- 16- 16- 15- 15- 15- 15- 14- 14- 14+ 14- -> 600 -> 200 400 600 200 400 600 200 400 200 400 600 The linear correlation coefficient is r= -0.971. (Round to three decimal places as needed.) The test statistic is t= - 7.036 . (Round to three decimal places as needed.) The P-value is (Round to three decimal…
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A professor was interested in how exam performance related to study time. Just before an exam began the professor asked students in his class to write down how many hours they had studied for the exam in the past two weeks. He then compared their exam scores to the reported study time. What type of study did the professor carry out? ex post facto correlational case experimental
. Dr. Hafen is doing research on the effects of study time (how many minutes students study) on test performance (their score on an exam). He hypothesizes that the amount of study time will impact an individual’s performance on the exam. Then Dr. Hafen collects data on 100 students. He collects data on their ‘study time’ and their ‘exam performance’, then runs a Pearson correlation. In your own words, please describe what Dr. Hafen’s null hypothesis would be and what Dr. Hafen’s alternative hypothesis would be. If Dr. Hafen makes a Type I error, what would that mean in the context of this study? If he makes a Type II error, what would that mean in the context of this study?
You wish to determine if there is a linear correlation between the age of a driver and the number of driver deaths. The following table represents the age of a driver and the number of driver deaths per 100,000. Use a significance level of 0.05 and round all values to 4 decimal places. Driver Age Number of Driver Deaths per 100,000 65 26 33 25 38 34 42 30 17 34 80 20 30 35 71 29 65 28 50 30 Но: р %3D 0 На: р 2 0 Find the Linear Correlation Coefficient r = Find the p-value p-value The p-value is O Less than (or equal to) a O Greater than a The p-value leads to a decision to O Reject Ho О Аcсеpt Ho O Do Not Reject Ho The conclusion is There is a significant linear correlation between driver age and number of driver deaths. O There is insufficient evidence to make a conclusion about the linear correlation between driver age and number of driver deaths. O There is a significant negative linear correlation between driver age and number of driver deaths. O There is a significant positive…

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