Question 1

Suppose you are analyzing the average ratings of CBC movies and want to compare them to the ratings of movies on two other networks, ABN and BBS. Which statistical test is most appropriate to determine if the mean rating of CBC movies is significantly different from the mean rating of ABN movies, assuming equal variances?

Accepted Answer

An independent samples t-test

Question 2

You are asked to construct a 95% confidence interval for the mean rating of CBC movies. Which of the following formulas should you use?

Accepted Answer

$\bar{x} \pm t_{0.025, n-1} \frac{s}{\sqrt{n}}$

Question 3

If the p-value from your t-test comparing CBC and ABN movie ratings is 0.03, and you are using a 95% confidence level, what is the correct interpretation?

Accepted Answer

There is sufficient evidence to reject the null hypothesis and conclude a difference in means.

Question 4

In a multiple regression analysis where the dependent variable is CBC movie ratings and the independent variables are star count and genre, what does a significant positive coefficient for star count indicate?

Accepted Answer

Movies with more stars tend to have higher ratings, holding genre constant.

Question 5

Which of the following is the correct null hypothesis for testing whether the mean rating of CBC movies is equal to the mean rating of ABN movies?

Accepted Answer

$H_0: \mu_{CBC} = \mu_{ABN}$

Question 6

Suppose your regression output for CBC movie ratings shows an $R^2$ value of 0.65. What does this mean?

Accepted Answer

65% of the variation in ratings is explained by the model.

Question 7

If the 95% confidence interval for the mean rating of CBC movies is (6.2, 7.8), what can you conclude?

Accepted Answer

We are 95% confident that the true mean rating of CBC movies is between 6.2 and 7.8.

Question 8

You are asked to compare the monthly average ratings for CBC over a year. Which graphical method is most appropriate to display the trend over time?

Accepted Answer

A line graph

Question 9

If you find that the regression coefficient for 'genre' is not statistically significant at the 95% confidence level, what does this imply?

Accepted Answer

Genre does not have a statistically significant effect on ratings at the 95% confidence level.

Question 10

Suppose you are forecasting future monthly ratings for CBC movies using a linear trend model. Which of the following equations best represents a linear trend forecast?

Accepted Answer

$\hat{y}_t = a + bt$

Question 11

If the standard deviation of CBC movie ratings is high, what does this indicate about the ratings?

Accepted Answer

The ratings are widely spread out from the mean.

Question 12

When comparing the average ratings of three networks (CBC, ABN, BBS), which statistical method should you use to test if at least one network has a different mean rating?

Accepted Answer

A one-way ANOVA

Question 13

If the regression output shows a p-value of 0.12 for the variable 'star count', what should you conclude at the 95% confidence level?

Accepted Answer

Star count is not statistically significant.

Question 14

Suppose you are asked to justify your recommendation to CBC executives based on your statistical analysis. Which of the following is the best approach?

Accepted Answer

Use the relevant statistical results and confidence intervals to support your recommendation.

Question 15

If you want to test whether the mean rating of CBC movies with stars is higher than those without stars, which is the correct alternative hypothesis?

Accepted Answer

$H_1: \mu_{stars} > \mu_{no\ stars}$

Question 16

Which of the following best describes the purpose of using a multiple regression analysis in the context of CBC movie ratings?

Accepted Answer

To estimate the effect of several independent variables on movie ratings simultaneously.

Question 17

If the confidence interval for the effect of 'star count' on ratings does not include zero, what does this imply?

Accepted Answer

Star count has a statistically significant effect on ratings.

Question 18

Suppose you are asked to evaluate which forecasting method is better for predicting monthly ratings: a linear trend or a 3-month moving average. Which criterion should you use?

Accepted Answer

The method with the lowest mean squared error (MSE).

Question 19

If you are asked to summarize your findings for CBC executives, which of the following should you include?

Accepted Answer

A clear summary of results, statistical evidence, and justified recommendations.

Statistical Analysis and Data Interpretation in Microeconomics: Case Study of CBC Movie Ratings

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