Final answer:
To compare the average number of cheesy lines in CSI: Miami and That's So Raven, a two-sample t-test can be performed. The average number of cheesy lines in That's So Raven is significantly higher than in CSI: Miami.
Step-by-step explanation:
To compare the average number of cheesy lines in the two TV shows, we can perform a Two-Sample t-test. The null hypothesis is that there is no significant difference between the averages, while the alternative hypothesis is that there is a significant difference. We can use a significance level of 0.05.
Step 1: Calculate the test statistic.
t = (mean1 - mean2) / sqrt((var1/n1) + (var2/n2))
Where mean1 and mean2 are the sample means, var1 and var2 are the sample variances, n1 and n2 are the sample sizes.
t = (11.3 - 17.5) / sqrt((3.1^2/20) + (4.8^2/15))
t = -6.2 / sqrt((0.482 + 0.818))
t = -6.2 / sqrt(1.3)
t = -6.2 / 1.14
t ≈ -5.44
Step 2: Determine the critical value.
For a two-sided test at a significance level of 0.05, we need to compare the absolute value of the test statistic to the critical value from the t-distribution with degrees of freedom equal to the smaller of (n1-1) and (n2-1).
Since the degrees of freedom for CSI: Miami is (20-1) = 19 and for That's So Raven is (15-1) = 14, we use the critical value from the t-distribution with 14 degrees of freedom.
The critical value at a 0.05 significance level is approximately 2.145.
Step 3: Make a decision.
Since the absolute value of the test statistic (5.44) is greater than the critical value (2.145), we reject the null hypothesis. This means that there is a significant difference in the average number of cheesy lines between CSI: Miami and That's So Raven.
Therefore, the correct option is 2) The average number of cheesy lines in That's So Raven is significantly higher than in CSI: Miami.