comment kimberly

  I NEED A POSITIVE COMMENT BASED IN THIS ARGUMENT..BETWEEN 150-200 WORDS

A level of significance is a value that we set to determine statistical significance. This is ends up being the standard by which we measure the calculated  p-value of our test statistic. To say that a result is statistically significant at the level alpha just means that the p-value is less than alpha.

For instance, for a value of alpha = 0.05, if the p-value is greater than 0.05, then we fail to reject the null hypothesis.

There are some instances in which we would need a very small  p-value to reject a null hypothesis. If our null hypothesis concerns something that is widely accepted as true, then there must be a high degree of evidence in favor of rejecting the null hypothesis. This is provided by a p-value that is much smaller than the commonly used values for alpha.

Alpha is the term used to express the level of significance we will accept. For 95% confidence, alpha=0.05. For 99% confidence, alpha=0.01. These two alpha values are the ones most frequently used. If our P-value, the high unlikeliness of the H 0, is less than alpha, we can reject the null hypothesis. Alpha and beta usually cannot both be minimized---there is a trade-off between the two. Ideally, of course, we would minimize both. Historically, a fixed level of significance was selected (alpha=0.05 for the social sciences and alpha=0.01 or alpha=0.001 for the natural sciences, for instance). This was because 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 H 0.

Example:  We took 10 samples of 20 pennies set on edge and the table banged. The resultant mean of heads was 14.5 with a standard deviation of 2.12. Since this is a small sample, and the population variance is unknown, after we calculate a t value and obtain t=6.71=(14.5-10)/(2.12/ (10)), we apply the t-test and find a P-value of either 8.73×10-5 or 4.36×10-5depending on whether we do a one-tailed or two-tailed test. In either case our results are statistically significant at the 0.0001 level.

Reference:

Calkins, Keith G. 2005. Applied Statistics Hypothesis Testing.  Retrieved from https://www.andrews.edu/~calkins/math/edrm611/edrm08.htm