Demand in any period that is outside the limits established by management policy. This demand may come from a new customer or from existing customers whose own demand is increasing or decreasing.

The term false negative for type I errors then would mean that the person does indeed have whatever was being tested for, but the test didn't find it. When testing for pregnancy, AIDS, or other medical conditions, both types of errors can be a very serious matter.

Alpha is the term used to express the level of significance we will accept. These two alpha values are the ones most frequently used. If our P-value, the high unlikeliness of the H0, is less than alpha, we can reject the null hypothesis.

Alpha and beta usually cannot both be minimizedthere is a trade-off between the two.

Ideally, of course, we would minimize both. This was due to the fact that the null hypothesis was considered the "current theory" and the size of Type I errors was much more important than that of Type II errors.

Now both are usually considered together when determining an adequately sized sample. Instead of testing against a fixed level of alpha, now the P-value is often reported. Obviously, the smaller the P-value, the stronger the evidence higher significance, smaller alpha provided by the data is against H0.

On July 14, we took 10 samples of 20 pennies set on edge and the table banged. The resultant mean of heads was In either case our results are statistically significant at the 0. The P-value of a test is the probability that the test statistic would take a value as extreme or more extreme than that actually observed, assuming H0 is true.

Power of a Test The power of a test against the associated correct value is 1-beta. It is the probability that a Type II error is not committed. There is a different value of beta for each possible correct value of the population parameter.

It also depends on sample size nthus increasing the sample size increases the power. Power is thus important in planning and interpretting tests of significance. It is easy to misspeak power 1-beta and P-value alpha. Power will be examined in greater detail in lesson 11 Hinkle chapter Setting the level of significance will correspond to the probability that we are willing to be wrong in our conclusion if a type I error was committed.

That probability will correspond to certain area s under the curve of a probability distribution. Those areas, known as the region of rejection is bounded by a critical value or critical values which are often computed.

Alternatively, one might compare the test statistic with the corresponding point s on the probability curve. These are equivalent ways of viewing the problem, just different units of measure are being used.

In a one-tailed test there is one area bounded by one critical value and in a two-tailed test there are two areas bounded by two critical values.

Which tail left or right under consideration for a one-tailed test depends on the direction of the hypothesis. Establishing the significance level and the corresponding critical value s is sometimes considered the second step in hypothesis testing.

Presumeably we have determined how the statistic we wish to test is distributed. This sampling distribution is the underlying distribution of the statistic and determines which statistical test will be performed.

Computing a Test Statistic Once the hypotheses have been stated, and the criterion for rejecting the null hypothesis establish, we compute the test statistic. The test statistic for testing a null hypothesis regarding the population mean is a z-score, if the population variance is known yeah right!

We used a t-score above, which is computing similarly, due to the small size of our sample and the fact that we do not know the population variance. We will have to examine other such test statistics and their underlying distributions.The standard deviation is a measure of the variability of values around the mean and is meant to be used with values that are normally distributed (e.g., follow a normal curve).

The standard normal curve is a bell-shaped curve. Introduction. Diagnostic x-rays contribute to nearly 50% of the total annual collective effective dose of radiations from man-made and natural sources to the general population in western countries; computed tomography (CT) is the largest single source of this medical exposure.

Normal Distribution For a finite population the mean (m) and standard deviation (s) provide a measure of average value and degree of variation from the average value. standard normal distribution from the area in the tails.

with a mean of inches and a standard deviation of inches. A study participant is randomly selected. a) Find the probability that his height is less than 66 inches.

sample means approximates a normal distribution. The greater the sample size, the better the approximation. where Φ is the cumulative distribution function of the standard normal distribution.

If Prob (XU) is extremely close to p 1, then Minitab uses the larger value between Prob (XU) to find sample size and accept number. Given two normally distributed populations with means, and, and variances, and, respectively, the sampling distribution of the difference,, between the means of independent samples of size and drawn from these populations is normally distributed with mean,, and variance, (/) + (/).

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