a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H₁: ?v #0 The p-value is: Round to 2 decimal places. (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 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 insignificant 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 use of the regression line is not appropriate. O here 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 I will have seeds with a lower sprout rate than a plant that produces fewer seeds.

Four Air Force trainee pilots take a test of visual acuity (higher scores mean better acuity) and an anxiety test (higher scores mean more anxiety. The scores are as follows: Person          Acuity (x)     Anxiety (y) 1                             1                     7     2                            1                      8 3                            2                      4 4                            4                     -1    Calculate critical value , SP the correlation coefficient  and determine whether the correlation is statistically significant  at the .05 significance level, two-tailed

Compute the Pearson correlation for the following data.X: 2, 3, 6, 4, 5 Y :3, 1, 5, 4, 2 A researcher is interested in seeing if there is a significant relationship between the number of hours of sleep a night (X) and Productivity scores (Y). She conducts a study to test her hypothesis. Please use the data set above.   Use a two-tailed test with a = 0.1. Conduct the four steps for hypothesis testing and label each step: Step1, Step 2, Step 3, and Step 4.

We compute a sample correlation coefficient of r=0.692 from a set of 12 data pairs. We are testing Ho:p=0 against H;:p#0 at a = 0.05. The value of the test statistic for this test is: O 3.18 O 3.64 O 3.03 3.94

Provide an interpretation for the following SPSS output: A researcher wanted to test the relationship between number of fries eaten per week and number of vegetables eaten per week by the sample. Number of times Number of times eat fries per eat vegetables week per week Number of times eat fries per Pearson Correlation 1 -.067 week Sig. (2-tailed) .005 N 1750 1750 Number of times eat Pearson Correlation -.067 1 vegetables per week Sig. (2-tailed) N .005 1750 1750 **Correlation is significant at the 0.01 level (2-tailed). Edit View Insert Format Tools Table 12pt v Paragraph

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The accompanying table lists the ages of acting award winners matched by the years in which the awards were won. 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. Should we expect that there would be a correlation? Use a significance level of = 0.05. E Click the icon to view the ages of the award winners. Construct a scatterplot. Choose the correct graph below. OA. OB. Oc. OD. 70- 70- Q 70- 70- ... ++++++ 20 - 20 Best Actress (years) 20- 70 20 Best Actress (years) 20- 20 Best Actress (years) 70 20 Best Actress (years) 70 70 Best Actresses and Best Actors Best Actress 27 29 30 58 33 34 46 30 62 22 44 51 D Best Actor 44 36 38 44 53 46 56 49 41 52 44 33

a) Compute the value of the sample correlation coefficient, r. (Round your answer to four decimal places.) r =  b) Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)   t = P- value = c) If a regression analysis were to be carried out to predict endurance from lactate level, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.) ____________   d) If a regression analysis were to be carried out to predict lactate level from endurance, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.) _____________

(i) State the hyptheses. (ii) Sketch a scatter plot tat best represents the data. (iii) Compute the value of the correlation coefficient. Round the answer to at least three decimal places. (iv) Find the P-value. Round the answer to at least four decimal places. Test the significance of r at α=0.05. Determine whether to reject or not reject the null hypothesis.

5.32 Fuel efficiency of manual and automatic cars, Part I: Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? Assume that conditions for inference are satisfied.   City MPG, Automatic City MPG, Manual Mean 16.12 19.85 SD 3.58 4.51 n 26 26 The test statistic is:The p-value is: