Use the Following Information to Answer the Question -Choose the Correct Null and Alternative Hypothesis to Test Whether

question 39

Multiple Choice

Use the following information to answer the question. A statistics professor is interested in learning whether there is a
positive association between number of posts by online students on a message board and the final class average in an online
statistics course. The computer output below shows the results from a regression model in which the final class average was
predicted by the number of message board posts. Assume that the conditions of the linear regression model are satisfied. $$\begin{array} { | l l | } \hline { \text { LinRegTTest for } y = a + b x } \\\hline \beta > 0 & a = 69.7104476 \\t = 3.707824045 & b = .8144278607 \\p = 0.0024306618 & s = 5.14275481 \\d f = 119 & r = .7774060152 \\\hline\end{array}$$
-Choose the correct null and alternative hypothesis to test whether there is an association between final class average and number of message board posts.

• A) \(\mathrm { H } _ { 0 }\) : There is a linear association between the number of message board posts and the final class average.
• \(\mathrm { H } _ { \mathrm { a } }\) : There is no linear association between the number of message board posts and the final class average.
• B) \(\mathrm { H } _ { 0 }\) : The correlation is positive.
• \(\mathrm { H } _ { \mathrm { a } }\) : The correlation is zero.
• C) \(\mathrm { H } _ { 0 }\) : There is no linear association between the number of message board posts and the final class average.
• \(\mathrm { H } _ { \mathrm { a } }\) : There is a positive linear association between the number of message board posts and the final class average.
• D) None of these.

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Definitions:

Paired Differences

Refers to the differences between paired observations in a sample, often used in statistical tests to analyze changes or effects in repeated measurements.

Degrees of Freedom

The number of independent values or quantities which can be assigned to a statistical distribution or to a system without violating any constraints.

Estimate

A rough calculation or judgment of the value, number, quantity, or extent of something.

Mean Difference

The average difference between two sets of data, often used to compare the mean values of two samples or measurements.