Deceptive News. In the article "When News Reporters Deceive: The Production of Stereotypes" (Journalism & Mass Communication Quarterly, Vol. 84, No. 2, pp. 281-298), 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?

Check whether or not the data provide sufficient evidence to conclude that an association exists between authenticity and tone.

Step 1:

The test hypotheses are given below:

Null hypothesis:

$H_0$: There is no association exists between authenticity and tone.

Alternative hypothesis:

$H_1$: There is an association exists between authenticity and tone.

Step 2:

Decide the level of significance.

Hence, the level of significance is $\alpha =0.05$

Step 3:

Find the expected frequency and test statistic.

MINITAB procedure:

Step a: Choose Stat > Tables > Chi-Square test for association.

Step b: In Columns containing the table, enter the column of Authentic and Deceptive.

Step c: In Rows, select Tone.

Step d: Under Statistics, select Chi-square test, Display counts in each cell, Display marginal counts and expected cell counts.

Step e: Click OK.

Now,

Minitab output:

From the MINITAB output, the value of the chi-square statistic is 10.427.

Step 4

Find the P-value.

From the MINITAB output, the P-value is 0.013.

Step 5:

Rejection rule:

If $P\text{-value≤a}$, then reject the null hypothesis.

Here, the P-value is lesser than the level of significance.

That is, $P\text{-value}(=0.005)<\alpha (=0.05)$.

Therefore, the null hypothesis is rejected at 5% level.

Thus, the results are statistically significant at $5\%$5% level of significance.

Thus, the data provide sufficient evidence to conclude that an association exists between authenticity and tone at the 5 % significance level.