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You want to know if something is going on (if there’ssome **effect**). You assume nothing is going on(**null hypothesis**), and you take a sample. You find theprobability of getting your sample if nothing is going on(**p-value**). If that’s too unlikely, you conclude thatsomething *is* going on (**reject the null hypothesis**). Ifit’s not that unlikely, you can’t reach a conclusion(**fail to reject the null**).

One particularly interesting application of hypothesis testing comes from the Royal Mint in England. The Royal Mint has been producing coins for more than 1,100 years. It currently produces coins for circulation in the United Kingdom, as well as commemorative coins. It also produces coins and medals for foreign governments.

**You always select a significance level before you know the p-value.**If you could first get the p-value and then specify a significancelevel, you could get whichever result you wanted, and there would beno point to doing a hypothesis test at all.

where the observed sample mean, μ_{0} = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences.

where the observed sample mean, μ_{0} = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences.

where the observed sample mean, μ_{0} = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences.

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_{0} = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences.

When you perform hypothesis testing, you only set the size of Type I error and guard against it. Thus, we can only present the strength of evidence against the null hypothesis. One can sidestep the concern about Type II error if the conclusion never mentions that the null hypothesis is accepted. When the null hypothesis cannot be rejected, there are two possible cases: 1) one can accept the null hypothesis, 2) the sample size is not large enough to either accept or reject the null hypothesis. To make the distinction, one has to check . If at a likely value of the parameter is small, then one accepts the null hypothesis. If the is large, then one cannot accept the null hypothesis.

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.

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.

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.

When testing hypotheses about a mean or mean difference, a *t*-distribution is used to find the p-value. This is a close cousin to the normal curve. T-Distributions are indexed by a quantity called degrees of freedom, calculated as df = n – 1 for the situation involving a test of one mean or test of mean difference.

When testing hypotheses about a mean or mean difference, a *t*-distribution is used to find the p-value. This is a close cousin to the normal curve. T-Distributions are indexed by a quantity called degrees of freedom, calculated as df = n – 1 for the situation involving a test of one mean or test of mean difference.

When testing hypotheses about a mean or mean difference, a *t*-distribution is used to find the p-value. This is a close cousin to the normal curve. T-Distributions are indexed by a quantity called degrees of freedom, calculated as df = n – 1 for the situation involving a test of one mean or test of mean difference.

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