Null and Alternative Hypotheses Example Problems ..

Under the null hypothesis, the statistic:   has a Chi-square distribution with d.f.

Statistics Problems: T-value, Z-value and Null Hypothesis

We do not reject H0 because -0.96 > -2.145. We do not have statistically significant evidence at α=0.05 to show that the mean total cholesterol level is lower than the national mean in patients taking the new drug for 6 weeks. Again, because we failed to reject the null hypothesis we make a weaker concluding statement allowing for the possibility that we may have committed a Type II error (i.e., failed to reject H0 when in fact the drug is efficacious).

The F-statistic is not large enough; therefore, one must reject the null hypothesis.

Hypothesis Testing Statistics Problems And Solutions

In sum, classical procedures employ the data to narrow down a setof hypotheses. Put in such general terms, it becomes apparent thatclassical procedures provide a response to the problem ofinduction. The data are used to get from a weak general statementabout the target system to a stronger one, namely from a set ofcandidate hypotheses to a subset of them. The central concern in thephilosophy of statistics is how we are to understand these procedures,and how we might justify them. Notice that the pattern of classicalstatistics resembles that of eliminative induction: in viewof the data we discard some of the candidate hypotheses. Indeedclassical statistics is often seen in loose association with Popper'sfalsificationism, but this association is somewhat misleading. Inclassical procedures statistical hypotheses are discarded when theyrender the observed sample too improbable, which of course differsfrom discarding hypotheses that deem the observed sampleimpossible.

The real question is in statistics not whether a null hypothesis is correct, but whether it is close enough to be used as an approximation.

The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic (e.g., reject H0 if Z > 1.645). The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below.

The next step is to compute the relevant statistic based on the null hypothesis and the random sample of size n.

Statistics hypothesis testing practice problems

4. Compare the -value to an acceptable significance value (sometimes called an ). If , that the observed effect is statistically significant, the null hypothesis is ruled out, and the alternative hypothesis is valid.

722-1 Hypothesis testing statistics problems and solutions

Notice that the top part of the statistic is the difference between the sample mean and the null hypothesis. The bottom part of the calculation is the standard error of the mean.

Null and Alternative Hypothesis | Real Statistics Using …

In general, a p-value is the probability that the test statistic would "lean" as much (or more) toward the alternative hypothesis as it does if the real truth is the null hypothesis.

Statistics Problems and Hypothesis Testing - BrainMass

If one or more of the sample sizes is less than 30 (as in this problem), a statistic is appropriate. The test statistic for this example is:

Perform the hypothesis test.

Statistics Problems and Hypothesis Testing

Hypothesis testing is similar. A claim has been presented, and the statistician must rule on the truth of the claim. Is the claim true or not? The evidence is collected in the form of a sample, and the statistician must then decide. There are two possible errors. The statistician could mistakenly reject a true null hypothesis (called a Type I error), or mistakenly accept a false null hypothesis (called a Type II error). The benefit of the doubt goes to the null hypothesis, which is assumed to be true until the evidence seems to indicate otherwise. The situation is summarized in the following chart.

answering the statistics and hypothesis testing problems

The second option is more active. If "failing to reject" $H_0$ is not a suitable conclusion, the statistician could enlarge the sample. By doing so, the variation in the sample distribution is reduced, making it easier to identify a false null hypothesis that was actually close to the parameter of the actual distribution. However, if the null hypothesis is actually true, no ground will be gained through the use of this option.