Which of the following denotes the strongest correlation? a. r = 0.54 b. r = -0.63 c. r = 0.43 d. r = .01
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- Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) Tip (dollars) 31.80 52.94 85.82 102.16 60.17 111.77 D 5.46 6.07 15.82 15.40 11.15 20.32 Construct a scatterplot. Choose the correct graph below. O A. O B. Oc. D. Q 25- 25- 25 0- 30 0- 30 Bill Amount ($) 0+ 30 Bill Amount (S) 0- 30 Bill Amount (S) 120 120 120 Bill Amount (S) 120 The linear correlation coefficient is r= 0.954 (Round to three decimal places as needed.) Determine the null and alternative hypotheses. Ho: p H,: P (Type integers or decimals. Do not round.) Tip Amount ($) ip Amount ($) Tip Amount ($) Tip Amount ($)The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a well-being test. Complete parts (a) through (d) below. LOADING... Click the icon to view the table of critical values of the correlation coefficient. a) Which variable is likely the explanatory variable and which is the response variable? Critical Values for Correlation Coefficient n 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 n (a) Which variable is likely the explanatory variable and which is the response variable? The explanatory variable is…A professor at the University of New Hampshire was interested in evaluating the effect of the unemployment rate on the incarceration rate. Using data from 50 states and the District of Columbia (n = 51), the researcher computed the Pearson’s correlation coefficient between the two variables. The results are presented below. Correlations Incarceration Unemployment Incarceration Pearson Correlation 1 .209 Sig. (2-tailed) .142 N 51 51 Unemployment Pearson Correlation .209 1 Sig. (2-tailed) .142 N 51 51 Using an alpha level of 0.05 and the four steps of the hypothesis testing process, test the research hypotheses that unemployment increases incarceration. Step 3 Step 4 Based on your decision to step 4 what type of error might you be making?
- You are a researcher interested in crime and crime rates. You’ve collected a sample of data from the county level for your state. You hypothesize that the rate of violent crimes will be higher in counties with bigger populations. Based on the below Pearson correlation results, is your hypothesis supported or rejected?A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below. Seeds Produced 68 56 61 Sprout Percent 60.6 69.2 = 0 48 64.7 64.6 #0 a. Find the correlation coefficient: b. The null and alternative hypotheses for correlation are: H₂: ? H₁: 2 The p-value is: 63 64.1 40 Round to 2 decimal places. 63 62 65.1 68.4 84 (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically significant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the regression line is useful. O There is statistically insignificant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds. O There is statistically significant…Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.05. Internet Users 79.0 78.3 56.9 68.7 77.2 38.6 Award Winners 5.4 9.2 3.2 1.8 10.6 0.1 Construct a scatterplot. Choose the correct graph below. O A. OB. с. 12- 12- 12,• 0- 30 30 90 Internet Users 30 90 Internet Users 30 Internet Users 90 90 Internet Users The linear correlation coefficient is r= (Round to three decimal places as needed.) Award Winners Award Winners
- A study was done to look at the relationship between number of partners college students have had in their lifetimes and their GPAs. The results of the survey are shown below. Partners 7 8 6 1 6 6 4 GPA 1.4 1.5 1.4 3 2.3 1.5 2.9 Find the correlation coefficient: r=r= Round to 2 decimal places. The null and alternative hypotheses for correlation are:H0:H0: ? r ρ μ Incorrect == 0 Ha:Ha: ? r ρ μ Incorrect ≠≠ 0 Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study. You may want to reference the 95% Critical Values of the Sample Correlation Coefficient. There is statistically insignificant evidence to conclude that there is a correlation between the number of partners students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that a student who has had more partners will have a lower GPA than a…For which of these research situations would you most likely calculate a Pearson's r correlation coefficient? independent variable = age; dependent variable = memory test score independent variable = type of car owned; dependent variable = money spent on gasoline per week independent variable = college major; dependent variable = GPA independent variable = city of residence; dependent variable = miles driven per weekA random sample of ten professional athletes produced the following data. The first row is the number of endorsements the athlete has and the second row is the amount of money made (in millions of dollars) by the athlete. What is the linear correlation coefficient? Round to three decimal places. Number of Endorsements 0 3 2 1 5 5 4 3 0 4 Profit (in Millions) 2 8 7 3 13 12 9 9 3 10
- grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below. Time 12 26 5 28 11 24 20 21 16 Money 37 84 34 84 53 92 72 92 75 Find the correlation coefficient: r=r= Round to 2 decimal places. The null and alternative hypotheses for correlation are:H0:H0: P == 0 H1:H1: P ≠≠ 0 The p-value is: (Round to four decimal places) r2 = (Round to two decimal places)Which of the following is an appropriate research question for a correlation? Group of answer choices Is there a relationship between weather and mood? Does cold weather impact mood? Does drinking milkshakes make children happy? Does exercising reduce weight?Which correlation value suggests the strongest correlation? 0.7 -0.1 O -0.8 O 0.4
