14. A correlation of r = .50 in a sample of 15 participants is statistically significant for a two-tailed test with α = .05. True False
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Q: What would our cutoff Z-score be if we want to do a two-tailed test and use an alpha of .01?
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- How large must a Pearson correlation coefficient, calculated on a sample of 22 people, be to be statistically significant at the alpha = 0.01 level in a two-tailed test (in other words, what is the critical value for the test)? .537 .472 .492 .515Researchers have collected data on the rate of BO disease from a random sample of persons across the country aged 50 and above (n = 250). In particular, researchers are curious in studying a claim made by the cig industry that there is a negative relationship between smoking cigarettes and the risk of contracting BO’s. The researchers have calculated a Pearson’s r correlation of −.709 for the two variables. The researchers have also calculated (using a computer) a significance value of .005.In a paragraph of five to six sentences, based on the results from the correlation, what conclusions can the researchers make about the relationship between smoking and getting BO’s? Ensure that you mention the unit of analysis, the direction of the relationship, the strength of the relationship, whether the findings are statistically significant, and how accurately the results would reflect the population. Do these findings support the cig industry’s claim? Why or why not?What are the hypotheses for testing to see if a correlation is statistically significant? Hor=0: H₁r0 Ho: p=0: H₁p0 Ho: p= ±1: H₁p #±1 Ho: p = 0; H₁:p=1 Ho: r = ±1; H₁: r#±1
- A researcher wants to know if male and female college students differ with regard to their GPAs. She randomly gets 16 male and 16 female college students to report their GPAs. The males reported a mean GPA of 3.05 with a SS = 3.75. The females reported a mean GPA of 3.1 with a SS = 2.4. You are going to be conducting an independent samples t-test. You will be conducting a two-tailed test with alpha α=.05. What is the critical t-value(s) for this test?A study is conducted involving 15 patients to investigate the relationship between their age and systolic blood pressure. Is the relationship between age and systolic blood pressure negative using Pearson correlation coefficient? yes or no or cannot be determined What is the strength of correlation between age and systolic blood pressure? weak, moderate, strong, or very strong If the tabulated value of r is equal to 0.514 at αα=0.05, what is the decision using Pearson r correlation? accept or reject HoFor a sample of n = 20 individuals, what correlation coefficient is necessary to be statistically significant at α =.05?
- will this be sufficient or is not sufficient evidence.Suppose X1,..., Xn is a random sample from an exponential distribution with mean e. If X = 17.9 with n = 50, find (a) a one-sided 95% confidence interval for 0, and (b) a two-sided 95% confidence interval for 0.42. When a correlation is sufficiently high, what statistic is used to predict the outcome of the dependent variable from a single independent variable? Stepwise comparison Bivariate regression Coefficient of determination
- 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?What is the interpretation of a Pearson's r correlation coefficient value of 0.8?Consider a regression analysis with n= 51 and four potential independent variables. Suppose that one of the independent variables has a correlation of 0.49 with the dependent variable. Does this imply that this independent variable will have a very small Student's t statistic in the regression analysis with all four predictor variables? Choose all that apply. A. The correlation between the independent variable and the dependent variable could result in a very small Student's t statistic as the correlation creates a high variance. B. Correlation between the independent variable and the dependent variable is not necessarily evidence of a small Student's t statistic. C. A high correlation among the independent variables could result in a very small Student's t statistic as the correlation increases the coefficient standard errors. D. Correlation between the independent variable and the dependent variable is evidence of a small Student's t statistic.
