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A small (p)-valueis an indication that the null hypothesis is false.

You can use the F statistic when deciding to support or reject the . In your F test results, you’ll have both an F value and an F critical value.

This is exactlyanalagous to choosing a significance level, (lpha),for test.

When you reject a null hypothesis, there's a chance that you're making a mistake. The null hypothesis might really be true, and it may be that your experimental results deviate from the null hypothesis purely as a result of chance. In a sample of 48 chickens, it's possible to get 17 male chickens purely by chance; it's even possible (although extremely unlikely) to get 0 male and 48 female chickens purely by chance, even though the true proportion is 50% males. This is why we never say we "prove" something in science; there's always a chance, however miniscule, that our data are fooling us and deviate from the null hypothesis purely due to chance. When your data fool you into rejecting the null hypothesis even though it's true, it's called a "false positive," or a "Type I error." So another way of defining the P value is the probability of getting a false positive like the one you've observed, if the null hypothesis is true.

Tests for one measurement variable

There are six parts of a test when using the rejection region approach:

Step 4. Find the appropriate critical values for the test using the z-table. Write down clearly the rejection region for the problem. We can use Table 2 to find the value of 0.025 since the row for df = (infinite) refers to the z-value.

Sometimes, you’ll be given a proportion of the population or a percentage and asked to support or reject null hypothesis. In this case you can’t compute a test value by calculating a (you need actual numbers for that), so we use a slightly different technique.

How to Determine a p-Value When Testing a Null Hypothesis

Rejection region: the set of values for the test statistic that leads to rejection of o.

A dairy farm uses the somatic cell count (SCC) report on the milk it provides to a processor as one way to monitor the health of its herd. The mean SCC from five samples of raw milk was 250,000 cells per milliliter with standard deviation 37,500 cell/ml. Test whether these data provide sufficient evidence, at the 10% level of significance, to conclude that the mean SCC of all milk produced at the dairy exceeds that in the previous report, 210,250 cell/ml. Assume a normal distribution of SCC.

Six coins of the same type are discovered at an archaeological site. If their weights on average are significantly different from 5.25 grams then it can be assumed that their provenance is not the site itself. The coins are weighed and have mean 4.73 g with sample standard deviation 0.18 g. Perform the relevant test at the 0.1% (1/10th of 1%) level of significance, assuming a normal distribution of weights of all such coins.

Step 0. Check the conditions for the one-proportion z-test to be valid:
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Step 3. Compute the value of the test statistic:


Example question:The average wait time to see an E.R. doctor is said to be 150 minutes. You think the wait time is actually less. You take a of 30 people and find their average wait is 148 minutes with a standard deviation of 5 minutes. Assume the distribution is normal. Find the p value for this test.

Critical Values of Chi-Square Distributions

Find the by looking up your answer from step 3 in the . To get the p-value, subtract the area from 1. For example, if your area is .990 then your p-value is 1-.9950 = 0.005. Note: for a two-tailed test, you’ll need to halve this amount to get the p-value in one tail.

Upper Critical Values of -Distributions

Compare your answer from step 4 with the α value given in the question. Should you support or reject the null hypothesis?
If step 7 is less than or equal to α, reject the null hypothesis, otherwise do not reject it.

Tests for multiple measurement variables

In the previous section hypotheses testing for population means was described in the case of large samples. The statistical validity of the tests was insured by the Central Limit Theorem, with essentially no assumptions on the distribution of the population. When sample sizes are small, as is often the case in practice, the Central Limit Theorem does not apply. One must then impose stricter assumptions on the population to give statistical validity to the test procedure. One common assumption is that the population from which the sample is taken has a normal probability distribution to begin with. Under such circumstances, if the population standard deviation is known, then the test statistic still has the standard normal distribution, as in the previous two sections. If is unknown and is approximated by the sample standard deviation , then the resulting test statistic follows Student’s -distribution with degrees of freedom.

Lower Critical Values of -Distributions

The asterisk system avoids the woolly term "significant". Please note, however, that many statisticians do not like the asterisk rating system when it is used without showing P values. As a rule of thumb, if you can quote an exact P value then do. You might also want to refer to a quoted exact P value as an asterisk in text narrative or tables of contrasts elsewhere in a report.

a. Use the rejection region approach to perform the testing.

The F statistic must be used in combination with the p value when you are deciding if your overall results are significant. Why? If you have a significant result, it doesn’t mean that all your variables are significant. The statistic is just comparing the joint effect of all the variables together.

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