• Perform a test for significance of slope and interpret the results
• Check the conditions that are necessary to perform a test for significance of slope

Let’s analyze the “Tomatometer” data. These data came from the movie ratings website Rotten Tomatoes^[1]. On this website, movie critics write reviews, and regular moviegoers submit ratings ([latex]1–5[/latex] stars) for movies and TV shows. We focused on [latex]125[/latex] movies from the website and the following variables.

• tomatometer: The “Tomatometer” score calculated as the percentage of professional movie and TV critics who write positive reviews for the movie
• audience_score: The percentage of the general public (regular moviegoers) who rate the movie [latex]3.5[/latex] stars or higher (out of [latex]5[/latex] stars)

Select “Movie Ratings” data set in the statistical tool below.

[Trouble viewing? Click to open in a new tab.]

Previously, you used the following test statistic to conduct a one-sample hypothesis test for the mean with [latex]H_0: \mu = \mu_0[/latex]:

[latex]t = \dfrac{\bar{x}-\mu_0}{[\text{std. error of }\bar{x}]}=\dfrac{\bar{x}-\mu_0}{\frac{s}{\sqrt{n}}}[/latex]

The slope of the population line, [latex]\beta_1[/latex], similarly follows a [latex]t[/latex] Distribution.

Test Statistics for the Hypothesis Test for Significance of Slope

The test statistic to test [latex]H_0: \beta_1 = 0[/latex] is:

[latex]t=\dfrac{b-0}{[\text{std. error of }b]} = \dfrac{b}{SE_b}[/latex]

---