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Five Steps in a Hypothesis Test

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.

Significance Tests / Hypothesis Testing

Null and Alternative Hypotheses for a Mean

The test statistic for examining hypotheses about one population mean:

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, μ0 = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences.

Hypothesis testing is generally used when you are

where the observed sample mean, μ0 = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences.

where the observed sample mean, μ0 = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences.

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See for more information about hypothesis testing.


Applying Hypothesis Testing in Business Statistics

where the observed sample mean, μ0 = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences.

Hypothesis will be available on

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.

Explore Hypothesis Testing in Business Statistics

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.

1. Testing of hypothesis on the variance of two normal populations.

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 hypothesis: μ = 72 Alternative hypothesis: μ ≠72

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 hypothesis: μ = 72 Alternative hypothesis: μ ≠72

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.

Write your hypotheses this way:

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.

Null and Alternative Hypotheses for a 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.

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