Question

In the article "When News Reporters Deceive: The Production of Stereotypes", researchers D. Lasorsa and J. Dai investigated the relationship between authenticity and tone for news stories. Tone was measured by using a method of coding sentences and was categorized as positive, neutral or negative. A sample of stories yielded the following data.

At the \(5%\) significance level, do the data provide sufficient evidence to conclude that an association exists between authenticity and tone?

Short answer

The data provide is sufficient evidence to conclude that an association exist between authenticity and tone.

Step-by-step solution

Step 1. Given information

The level of significance \(\alpha =0.05\)

Step 2. Calculation

Consider the below test hypothesis.

Null hypothesis:

\(H_{0}\):There is no association between authenticity and tone.

Alternative hypothesis:

\(H_{a}\): There is association between authenticity and tone.

By using any software perform the chi-square homogeneity test to find the test statistic.

Enter the given data,

Then we get, the chi-square static as \(=10.427, p-value=0.005\).

Then, we have the

The rejection rule:

\(p-value \leq \alpha\), then null hypothesis rejected.

The level of significance \(\alpha =0.05\)

Here , clearly \(p-\)value is less than the level of significance.

\(p-value (0.005)<\alpha (0.05)\)

So, the null hypothesis is rejected at \(5%\) significant level.

Thus the results are statistically significant at \(5%\) significant level.

Hence,

The data provide is sufficient evidence to conclude that an association exist between authenticity and tone.