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Hypothesis Testing for Means & Proportions

One possible conclusion to a statistical hypothesis test. We use this phrase since, using our process, we cannot prove the null hypothesis. In this case the data from our sample would not be rare if the null hypothesis were true and thus we cannot reject the null hypothesis.

H0: Null hypothesis (no change, no difference);

Hypothesis testing applications with a continuous outcome variable in a single population are performed according to the five-step procedure outlined above. A key component is setting up the null and research hypotheses. The objective is to compare the mean in a single population to known mean (μ0). The known value is generally derived from another study or report, for example a study in a similar, but not identical, population or a study performed some years ago. The latter is called a historical control. It is important in setting up the hypotheses in a one sample test that the mean specified in the null hypothesis is a fair and reasonable comparator. This will be discussed in the examples that follow.

I’m stuck on how to value the null or alternative hypotheses

Im having a hard time answer a problem. The genetics and IV I situate conduct a clinical trial of the YOSORT method designed to increase the probability of a boy and 239 of them were Boyd’s. Use a 0.01 significance level to test the claim that the YOSORT method is effective in increasing the like hood that a baby will be a boy . I have to identify the null hypothesis, alternative hypothesis, test status is, p-value or critical value .

No-one I know can figure out which statistical test(s) I can do with the results, basically I have 4 tables of data that I tested for 12 hours (Once an hour eg 1900 – 1959, 2000 – 2059 etc…) for 30 days.
The light levels, humidity levels and temperature I need to compare with the ewes entering parturition data, I’ve calculated the means and standard deviation but, I get mixed results when I then run an ANVOVA test, t test two sample assuming equal variances and an f test two sampled for variances

We reject the null hypothesis because -6.15

In one sample tests for a continuous outcome, we set up our hypotheses against an appropriate comparator. We select a sample and compute descriptive statistics on the sample data - including the sample size (n), the sample mean ( ) and the sample standard deviation (s). We then determine the appropriate test statistic (Step 2) for the hypothesis test. The formulas for test statistics depend on the sample size and are given below.

In all tests of hypothesis, there are two types of errors that can be committed. The first is called a Type I error and refers to the situation where we incorrectly reject H0 when in fact it is true. This is also called a false positive result (as we incorrectly conclude that the research hypothesis is true when in fact it is not). When we run a test of hypothesis and decide to reject H0 (e.g., because the test statistic exceeds the critical value in an upper tailed test) then either we make a correct decision because the research hypothesis is true or we commit a Type I error. The different conclusions are summarized in the table below. Note that we will never know whether the null hypothesis is really true or false (i.e., we will never know which row of the following table reflects reality).

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the null hypothesis is rejected when it is true b.

We now use the five-step procedure to test the research hypothesis that the mean weight in men in 2006 is more than 191 pounds. We will assume the sample data are as follows: n=100, =197.1 and s=25.6.

the null hypothesis is not rejected when it is false c.

In all tests of hypothesis, there are two types of errors that can be committed. The first is called a Type I error and refers to the situation where we incorrectly reject H0 when in fact it is true. This is also called a false positive result (as we incorrectly conclude that the research hypothesis is true when in fact it is not). When we run a test of hypothesis and decide to reject H0 (e.g., because the test statistic exceeds the critical value in an upper tailed test) then either we make a correct decision because the research hypothesis is true or we commit a Type I error. The different conclusions are summarized in the table below. Note that we will never know whether the null hypothesis is really true or false (i.e., we will never know which row of the following table reflects reality).

the research hypothesis is not rejected when it is false722-1

We now use the five-step procedure to test the research hypothesis that the mean weight in men in 2006 is more than 191 pounds. We will assume the sample data are as follows: n=100, =197.1 and s=25.6.

the null hypothesis is probably wrong b.

Statistical computing packages provide exact p-values as part of their standard output for hypothesis tests. In fact, when using a statistical computing package, the steps outlined about can be abbreviated. The hypotheses (step 1) should always be set up in advance of any analysis and the significance criterion should also be determined (e.g., α =0.05). Statistical computing packages will produce the test statistic (usually reporting the test statistic as t) and a p-value. The investigator can then determine statistical significance using the following: If p α then reject H0.

the result would be unexpected if the null hypothesis were true c.

Krista,
I’m not sure what your question is. You list quite a few (identify null, alternate, test status, p-value or critical). Are you having trouble identifying the null and alternate hypotheses? Or is it that you don’t know what test to run?
BTW: both the critical value and p-value will give you the same results. I’d just choose one and go from there.
Stephanie

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