Which of the following correctly states the null hypothesis?     Ho: There is no correlation between cognitive reflectivity and gray-matter density     Ho: There is a correlation between cognitive reflectivity and gray-matter density     Ho: Gray matter density is independent of cognitive strategies     Ho: Gray matter density is dependent on cognitive strategies     Ho: The two groups are equivalent or cannot be distinguished.

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.

In this problem, we use your critical values table to explore the significance of r based on different sample sizes.

A 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 25 8 24 6 18 16 7 12 Money 82 18 106 40 64 50 22 60     The null and alternative hypotheses for correlation are:H0:H0: ? r μ ρ Correct = 0H1:H1: ? ρ r μ Correct  ≠ 0    The p-value is:            (Round to four decimal places) 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. There is statistically insignificant evidence to conclude that there is a correlation between the amount of time customers spend at the store and the amount of money that they spend at the store. Thus, the use of the regression line is not appropriate. There is statistically insignificant evidence to conclude that a customer who spends more time at the store will spend more money than a customer who spends…

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