Question

(4) 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 sample standard deviation of 4.2 min utes. At a 0.10 , is the sample standard deviation different from what the editor hypothesized?

Answer 1

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H₀: σ = 3.4

H_a: σ ≠ 3.4

(2) Rejection Region

Based on the information provided, the significance level is α = 0.10 and and degrees of freedom (df) = 24 -1 = 23

Thus, the rejection region for this two-tailed test is R = {χ²: χ² < 13.091 or χ² > 35.172}

(3) Test Statistics

The Chi-Squared statistic is computed as follows:

y2= (n - 1)s2 The test statistic is

Here, n = 24, s = 4.2, and σ₀ = 3.4

χ² = (24-1)*(4.2*4.2)/(3.4*3.4)

χ² = 35.096

(4) Decision about the null hypothesis

Since it is observed that χ_L²​ = 13.091 < χ2 = 35.097< χ_U² ​= 35.172, it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the standard deviation is different than what the editor hypothesized, at the 0.10 significance level.