Question 1189355: One variable that Google uses to rank pages on the Internet is page speed, the time it takes for
a web page to load into your browser. A developer for women’s clothing company is
redesigning their page to improve the images that show its products and to reduce its load
time. The new page is clearly faster, but initial tests indicate there is more variation in the time
to load. A sample of 16 different load times showed that the standard deviation of the load
time was 22 hundredths of a second for the new page and 10 hundredths of a second for the
current page. At the .05 significance level, can we conclude that there is more variation in the
load time of the new page
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to conduct an F-test to compare the variances of the load times for the two web pages:
**1. State the Hypotheses:**
* Null Hypothesis (H₀): The variances of the load times for the new page and the current page are equal. σ₁² = σ₂² (where σ₁² is the variance of the new page and σ₂² is the variance of the current page).
* Alternative Hypothesis (H₁): The variance of the load time for the new page is greater than the variance of the load time for the current page. σ₁² > σ₂² (We're testing for *more* variation, so it's a one-tailed test.)
**2. Determine the Level of Significance:**
α = 0.05 (given)
**3. Calculate the F-Statistic:**
The F-statistic is the ratio of the larger sample variance to the smaller sample variance. In this case:
F = s₁² / s₂²
Where:
* s₁² = sample variance of the new page = (22)² = 484
* s₂² = sample variance of the current page = (10)² = 100
F = 484 / 100 = 4.84
**4. Determine the Degrees of Freedom:**
* df₁ = n₁ - 1 = 16 - 1 = 15 (numerator degrees of freedom)
* df₂ = n₂ - 1 = *We don't have n₂ for the current page. We will assume it is large enough that it does not impact the result.*
**5. Find the Critical Value:**
Using an F-distribution table or calculator, look up the critical value for a one-tailed test with α = 0.05, df₁ = 15, and a large df₂. The critical value is approximately 2.40.
**6. Make a Decision:**
* Compare the calculated F-statistic to the critical value: Our calculated F (4.84) is greater than the critical value (2.40).
* Conclusion: Because our F-statistic exceeds the critical value, we reject the null hypothesis.
**7. Interpret the Results:**
There is sufficient evidence at the 0.05 significance level to conclude that there is more variation in the load time of the new web page compared to the current web page.
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