Topics

• Conduct a hypothesis test for β1

• Calculate a confidence interval for β1

Movie ratings data

The data set contains the "Tomatometer" score (critics) and audience score (audience) for 146 movies rated on rottentomatoes.com.

The model

model <- lm(audience ~ critics, data = movie_scores)

model %>%
  tidy() %>%
  kable(format = "html", digits = 3)

The model

^audience=32.316+0.519×critics

Outline of a hypothesis test

1️⃣ State the hypotheses.

2️⃣ Calculate the test statistic.

3️⃣ Calculate the p-value.

4️⃣ State the conclusion.

1️⃣ State the hypotheses

1️⃣ State the hypotheses

1️⃣ State the hypotheses

2️⃣ Calculate the test statistic

2️⃣ Calculate the test statistic

3️⃣ Calculate the p-value

Calculated from a t distribution with n−2 degrees of freedom

3️⃣ Calculate the p-value

Understanding the p-value

These are general guidelines. The strength of evidence depends on the context of the problem.

4️⃣ State the conclusion

The data provide sufficient evidence that the population slope β1 is different from 0.

There is a linear relationship between the critics score and audience score for movies on rottentomatoes.com.

Confidence interval for β1

t∗ is calculated from a t distribution with n−2 degrees of freedom

Calculating the 95% CI for β1

ˆβ1=0.519t∗=1.977SEˆβ1=0.035

Interpretation

We are 95% confident that for every one point increase in the critics score, the audience score is predicted to increase on average between 0.450 and 0.588 points.

Recap

• Conducted a hypothesis test for β1

• Calculated a confidence interval for β1