Question

In: Statistics and Probability

Give a mean and standard deviation that would indicate a majority of children are on their...

Give a mean and standard deviation that would indicate a majority of children are on their phones between 1.3 and 3.3 hours a day.

What is the relationships of a critical value to an observed value in a t test and ANOVA? Where do you find them and what do they mean?

Is it possible that you could satisfy both p < .01 and p< .05? Is it possible to only have one or the other exclusively? Explain.

What are the hypothesis tests that make up an ANOVA? What is the purpose of the test? What is an example of a question that you would ask with an ANOVA? What is an example of a situation that would require you to use t tests and an ANOVA? What are those t tests called? When would you use an ANOVA but not use t tests?

Let’s say that we are testing the effect of distance on self-disclosure. The distances are 2, 4, or 6 ft. The interviewer measures the number of personal, revealing statements made by the subject. Complete the ANOVA and the summary Table below. Is the F value significant at the .05 level? Is it significant at the .01 level? What are the critical and observed values? What do they mean?

Compute the Pearson Correlation Coefficient ( r ) in the problem below. Is it significant? What does that mean? What are the critical values and observed values? What do those mean? What is the relationship – positive or negative? What does that mean?

What is an example of a positive relationship and negative relationship that you have seen in the news? What is an examples of an illusory correlation? Why do people say ‘correlation is not causation’?

Solutions

Expert Solution

Give a mean and standard deviation that would indicate a majority of children are on their phones between 1.3 and 3.3 hours a day.

Answer: The mean and standard deviation would be 2.0 hours and 0.5 hours respectively.

What is the relationships of critical value to an observed value in a t test and ANOVA? Where do you find them and what do they mean?

Answer: The critical is the cut off value for the observed value in a t test and ANOVA. If the critical value is less than the observed value then we reject the null hypothesis otherwise it is not rejected. Critical values are found by using the t-distribution table for t-test and F-distribution for ANOVA and these values are based on the distribution of the degrees of freedom for the test.

Is it possible that you could satisfy both p < .01 and p< .05? Is it possible to only have one or the other exclusively? Explain.

Answer: Yes, it is possible that we can satisfy both p < .01 and p< .05, if the p-value is less than 0.01 then it will automatically satisfy p< .05. No, they can be exclusively satisfied as well, if p value is greater than .01 but less than .05 then p < .05 is exclusively satisfied. But if p value is less .01 then both relations will be satisfied.

What are the hypothesis tests that make up an ANOVA? What is the purpose of the test? What is an example of a question that you would ask with an ANOVA? What is an example of a situation that would require you to use t tests and an ANOVA? What are those t tests called? When would you use an ANOVA but not use t tests?

Answer: The F-test for the difference in means make up an ANOVA. The purpose of the test is to use compare the groups in ANOVA. An example question would be, whether the mean salary of high-school, graduate, post-graduate, and Ph.D. students are significantly different from each other or not. The t-tests are used when we have one group or two groups like comparing the mean of high-school students from a threshold value say $8000, the difference in mean salary of high-school and graduate students, also we can measure the mean salary of graduate students after graduation and after 5 years of experience using t-test, on the other hand, an ANOVA will be used if we want to compare all the educational groups mean. The t tests are one-sample t test, independent t-test, and paired t-test. We will use ANOVA but not t tests when we have more than two groups.

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