Question

Write your thoughts on this discussion.

Hypothesis testing is a statistical tool useful for ascertaining information about a specific conclusion. Specifically, this type of testing can help with understanding a data set (population) and the samples of data used to make assertions about those populations. The general process for testing a hypothesis involves selecting a particular element of a population such as the "mean, proportion, standard deviation, or variance" (Evans, p139) and then looking for a contrasting detail to compare with the original supposition or hypothesis. In greater detail, select a hypothesis and one that contrasts with the original (alternate hypothesis), then determine what outcome could occur if the original hypothesis is incorrect. Figure out the criteria for deciding if its true or not. Get data, then apply the that criteria to the data and determine if the hypothesis test results in a positive or negative finding. Parametric Hypothesis testing is a method of testing population data where the data is supposed to fall into a normal distribution. A normal distribution is the "bell-shaped curve." Nonparametric hypothesis testing is done where the data a presumably not a "normal" distribution. In other words will be some other shape that the bell-shaped curve.

Answer 1

One-Sample z-test

Requirements: Normally distributed population, σ known

Test for population mean

Hypothesis test

Formula:

where is the sample mean, Δ is a specified value to be tested, σ is the population standard deviation, and n is the size of the sample. Look up the significance level of the z‐value in the standard normal table

Example

A herd of 1,500 steer was fed a special high‐protein grain for a month. A random sample of 29 were weighed and had gained an average of 6.7 pounds. If the standard deviation of weight gain for the entire herd is 7.1, test the hypothesis that the average weight gain per steer for the month was more than 5 pounds.

null hypothesis: H 0: μ = 5

alternative hypothesis: H a: μ > 5

Tabled value for z ≤ 1.28 is 0.8997

p value = 1 – 0.8997 = 0.1003

So, the conditional probability that a sample from the herd gains at least 6.7 pounds per steer is p = 0.1003. Should the null hypothesis of a weight gain of less than 5 pounds for the population be rejected? That depends on how conservative you want to be. If you had decided beforehand on a significance level of p < 0.05, the null hypothesis could not be rejected.

( NOTE - If p value is less than then the level of significance (alpha), then we reject the null hypothesis, otherwise we fail to reject the null hypothesis )