# How can you use the ANOVA to reject a null hypothesis? How is it related to the F-critical value?

If the null hypothesis criteria are not met by the relevant calculations (compared to the F-value) then it must be rejected.

It is important to note that ALL statistical ‘tests’ relate to some continuous function of probabilities. It remains to the individual to decide what level of ‘uncertainty’ (and risk) they can live with. There is no “magic number” that is deterministic. Whether the probability of rain is 10% or 90%, it MIGHT rain! Only the individual can evaluate the cost/benefit ratio of going out for picnic or not. Some will go where others will not.

Related to that is the supreme importance of a properly stated hypothesis!! In most cases, it must ask/answer ONLY ONE question – yes/no, based on your risk/uncertainty value. One can lead to another, but anytime more than one question/condition is asked in a hypothesis statement, the answers will be ambiguous at best, and worthless at worst.

The various tests, critical values and names are related to the specific types of calculations and distribution curves expected. They all result statistically in the same outcome – am I willing to accept my hypothesis as more likely than random occurence, or not.

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To reject a null hypothesis using ANOVA, you compare the calculated F-value (F-statistic) obtained from the ANOVA test to the critical F-value. If the calculated F-value is greater than the critical F-value, you reject the null hypothesis. The F-critical value is determined based on the significance level (alpha) chosen for the test and the degrees of freedom associated with the numerator and denominator of the F-distribution. If the calculated F-value exceeds the critical F-value, it indicates that there is a significant difference between the means of the groups being compared, and you reject the null hypothesis in favor of the alternative hypothesis.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A machine is programmed to put 737g of salts in each container that passes underneath its nozzle.In order to test Hnull:#mu#=737 vs Ha:#mu#>737, a sample of 100 boxes of salt is selected.How large must the sample mean be before the Hnull can be rejected?
- How can you use the ANOVA to reject a null hypothesis? How is it related to the F-critical value?
- Men ages(20-29) have meanheight 69.3 with s.dev of 2.5 in. An analyst wonders if sd of majorleague players less than 2.5 in. Heights of 20 random players are:72, 74, 71, 72,76,70,77,75,72,72,77,73,75,70,73,74,75,73,74,73. Can you help me find the P value?
- H0: μ = 100 H1: μ ≠ 100 σ = 10,𝑛 = 100,𝑥̅ = 100,𝛼 = 0.05 Calculate the value of the test statistic, set up the rejection region, determine the p-value, interpret the result, and draw the sampling distribution. How?
- If the mean time between in-flight aircraft engine shutdowns is 12500 operating hours, the 90th percentile of waiting times to the next shutdown will be?

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