A hypothesis test is conducted to compare the sample standard deviation with the editor's hypothesis. The test assesses if the sample standard deviation of 4.2 minutes significantly differs from the hypothesized 3.4 minutes at a 0.05 significance level.
To determine if the sample standard deviation significantly differs from the editor's hypothesis, a hypothesis test is conducted. The null hypothesis (H0) posits that the sample standard deviation is equal to the hypothesized standard deviation (σ0), and the alternative hypothesis (Ha) suggests that they are different.
Mathematically, H0: σ = σ0 and Ha: σ ≠ σ0.
The test statistic for comparing sample standard deviation (s) with the hypothesized standard deviation (σ0) follows a chi-square (χ^2) distribution. The formula for the test statistic is χ^2 = (n-1)s^2/σ0^2, where n is the sample size.
In this scenario, with 24 videos (n = 24), sample standard deviation s = 4.2, and hypothesized standard deviation σ0 = 3.4, we can compute the test statistic.
If the computed χ^2 exceeds the critical value from the chi-square distribution with n-1 degrees of freedom, we reject the null hypothesis. At a significance level (α) of 0.05 and a two-tailed test, the critical values are found in the chi-square distribution table.
In summary, the hypothesis test will assess whether the sample standard deviation of 4.2 minutes significantly differs from the editor's hypothesis of 3.4 minutes, providing insights into the variability in video lengths.
The question probable may be:
A film editor feels that the standard deviation for the number of minutes in a video is 3.4 minutes. A sample of 24 videos has a standard deviation of 4.2 minutes. At α = .05, is the sample standard deviation different from what the editor hypothesized?