What Is a Hypothesis?A hypothesis is a statement about a population. Data are then used to check thereasonableness of the statement.

State the Null Hypothesis and the Alternate Hypothesis

Select a Level of Significance

Select the Test StatisticThere are many test statistics. In this chapter, we use both z and t as the test statistic.

Formulate the Decision Rule

Make a Decision

IMP

Finding critical value of z:normsinvIf you enter 0.975 , your output is 1.96 (rounded)

z a/2 -- Do you mean a two-tailed z value with a level 0.05?Then, subtract a/2 from 1. Enter that probability in Excel and read the output below.Example:z 0.01/2 = z .005Enter 0.995 and read off 2.5758IMP

A One-Tailed Test

p-Value in Hypothesis Testing

Calculating P-value

These areas and the p-value can be found in Excel using the NORMSDIST(-3) function, in the z-table, or with the Excel utility provided

.

In the below case the area can be found by using excel NORMSDIST(-1.55) for NORM.S.DIST(-1.55,true(cumulative distribution funcation2*(.0606)=.1212

Confidence level is increasing

Super imp

But the p-value 0.0027 is much smaller than 0.05. Thus, we can reject the null hypothesis at 0.0027, a much lower significance level. In other words, we can reject the null hypothesis with 99.73% confidence. In general, the lower the p-value, the higher our confidence in rejecting the null hypothesis.

Testing for a Population Mean:Population Standard Deviation Unknown

a one-tailed area of 0.05 with 39 degrees of freedom:

The right function isTINV(), but the problem is thatTINV()assumes that you're inputting the two-tailed probability, not the one-tailed probability.

Thus if you wantTINV()to give you the critical value associated with a one-tailed probability, you have to double the probability first to account for the other tail. Thus, for example,TINV(0.1,39)yields an output of1.684875122, which is the critical value you want.

10.9 Tests Concerning Proportions

TYPE 1 and Type 2 errors from book