Reference all sources. ZERO PLAGIARISM
Write a summary (with formula or explaining the example of F test (var.test) shown below:
1. What is the purpose of the F test (VAR Test) ?
where it is used
Who use it
2. What is calculated in the test ?
3. What are the assumptions of the test ?
4. Explain each how to interpret the following items in the output of var.test():
…4.1… F = 0.332
…4.2… num df = 9, denom df = 19
…4.3… p-value = 0.094
…4.4… alternative hypothesis: true ratio of variances is not equal to 1
…4.5… 95 percent confidence interval: 0.11519 1.22196
…4.6… sample estimates: ratio of variances 0.33175
5. In the example below:
x <- runif(n=10, min=6, max=10)
y <- runif(n=20, min=12, max=18)
# F test to compare two variances
# data: x and y
# F = 0.332, num df = 9, denom df = 19, p-value = 0.094
# alternative hypothesis: true ratio of variances is not equal to 1
# 95 percent confidence interval:
# 0.11519 1.22196
# sample estimates:
# ratio of variances
Answer the following:
5.1… what is the null hypothesis Ho? Explian. What is the null hypothesis in this example?
5.2… what is the significance level? Explian. What is the significance level in this example?
5.3… having compared the p-value with the significance level, should we reject Ho?
5.4… having compared the sample estimate and the confidence interval, should we reject Ho? (hint: are the sample estimate and confidence interval obtained from the same data?)
5.5 having compared the hypothesized ratio of the population variances of x and y and the confidence interval, should we reject Ho?
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