12) As we have noted in previous chapters, even a very small effect can be significant if the sample is large enough. Suppose, for example, that a researcher obtains a correlation of r = .600 for a sample of n = 10 participants. a) Is this sample sufficient to conclude that a significant correlation exists in the population? Use a two-tailed test with a = .05. b) If the sample had n = 25 participants, is the correlation significant? Again, use a two- tailed test with a = .05.

For a data set of brain volumes ​(cm3​) and IQ scores of five ​males, the linear correlation coefficient is found and the​ P-value is 0.619. Write a statement that interprets the​ P-value and includes a conclusion about linear correlation. The​ P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is nothing​%, which is ▼   high, low, so there ▼   is is not sufficient evidence to conclude that there is a linear correlation between brain volume and IQ score in males. ​(Type an integer or a decimal. Do not​ round.)

2. If the correlation coefficient is 0.930, what is the unexplained variation? A 86.5% B. 93% C. 7% D. 13.5%

In what situations can a point-biserial correlation be used? Group of answer choices When a single-sample t test would also be appropriate. When both X and Y are ranks. When both X and Y are dichotomous. When an independent-measures t test would also be appropriate.

A study of bone density on 5 random women at a hospital produced the following results. Age    41    45    49    69    73Bone Density    360    350    345    335    330 Step 3 of 3: Calculate the coefficient of determination, r2. Round your answer to three decimal places.

will this be sufficient or is not sufficient evidence.

1. for a two tailed with a=.05, use table b.6 to determine how large a pearson correlation is necessary to be statistically significant for each of the following samples? a. A sample of n=6 b. A sample of n=12 c. A sample of n=24

Which of the following is not a cause of perfect multicollinearity? Select all that apply. One of the explanatory variables is equal to half of another explanatory variable for 100% of the observations in the sample. The correlation between two of the explanatory variables is 1.00. One of the explanatory variables is equal to half of another explanatory variable for 20% of the observations in the sample. A dummy variable for male is included at the same time as a dummy variable for non-male. One of the regressors is X and another regressor is X².

Are there ever any circumstances when a correlation such as Pearson’s r can be interpreted as evidence for a casual connection between two variables? If yes, what circumstances?

An Economics instructor assigns a class to investigate factors associated with the gross domestic product (GDP) of nations. Each student examines a different factor (such as life expectancy, literacy rate, etc.) for a few countries and reports to the class. Apparently, some of the classmates do not understand Statistics very well because several of their conclusions are incorrect. Explain the mistakes in comments a and b below. a) Explain the mistake in the statement "There was a very strong correlation of 1.22 between Life Expectancy and GDP" Choose the correct answer below O A. A correlation cannot be greater than 1. O B. A correlation that is greater than 1 implies that the variables are not quantitative, so the correlation cannot be interpreted. OC. A correlation that is close to 1 implies a very weak correlation. The correlation must be close to 10 for it to be interpreted as a very strong correlation. O D. A correlation that is greater than 1 implies a weak correlation, not a…