Ch9 one page handout: Hypothesis testing

Write the hypothesis statement

Condition statement: / Ho Sign / Ha Sign / Condition statement: / Ho Sign / Ha Sign
less than or equal to; at-most / ≤ / Less than; decreased / ≥
greater than or equal to; at-least / ≥ / Greater than; increased / ≤
equal to; not equal to; different from; is; is not / = / ≠ / Note: In all the situations, equality sign is always with H0 only

There can be no gap, or overlap between H0 and Ha. Ho and Ha always refer to the population parameter such as population mean (µ), or population proportion (p)

One tail or two tail

If the Ha sign is <, then it is also called lower tail or left tail test; If the Ha sign is >, then it is called upper tail or right tail test; If the Ha sign is ≠, then it is called two tail test.

Remember to draw the sketch of the normal distribution and then show the H0 and Ha areas accordingly

Box 1: Collect sample statistics e.g., sample mean, sample size, standard deviation etc.

Box 2: Compute the test statistics(use the information given in box 1 and the formula shown below)

Use the formula given below to compute the z or t statistics (first two are for means, last one is for proportions)

(1)Means(make sure that the sample size is atleast 30 or that the population distribution is a normal distribution; the ideea is that the sampling distribution should be a normal distribution) / (2)Proportions
Make sure n>5 and n(1-)>5 in order for sampling distribution to be a normal distribution
Population std deviation
known / Population std deviation unknown

(Note:  represents population std dev) /
(Note: s represents sample std dev) /
(Note: p represents population proportion and represents sample proportion)

Box 3

Use the Zstat or Tstat value obtained above, then use the Z or T table (respectively) to find the p value

In case of Z, for p values refer to the area from the Z table corresponding to negative Z(Just always use – Z side of Table)

In case of T, for p values refer to the area from the T table corresponding to positive T

If it is two tail test, then multiply the area from the table by 2 to get the p value.

Box 4

Remember: alpha =  = significance level = (1 – confidence level in decimal form); By default, alpha = .05.

Box 5 (contains Z or Tfor one tail test; and +T/2–T/2 or +Z/2 –Z/2 for two tail tests)

Use the alpha (from Box 4) and treat it as probability and find the corresponding T or Z value from the table. The value in Box 5 i.e. Z or T is positive for upper tail test, and negative for lower tail test. For two tail test, first divide the alpha by 2, and then find the Z or T value accordingly. For two tail tests you need to report both +Z/2 and –Z/2or +T/2 and –T/2 in Box 5.

Conclusion

You can find conclusion either with p-value approachi.e. by comparing box 3 and box 4; or by critical value approachi.e. by comparing box 2 and box 5.

P value approach: Compare the p value (box 3) with alpha (usually .05) from box4. If p value is less than alpha, then reject H0, otherwise conclude fail to reject H0.

Critical value approach: Compare box 2 and box 5. If absolute value of box 2 is more than absolute value of box 5, then reject H0. For two tail test: reject H0 if absolute value of box 2 is more than positive Z/2 or T/2.

Business Decision

When rejecting H0, conclude that we have the evidence to go according to the statement mentioned in Ha

When failing to reject H0, conclude that we don’t have enough evidence to conclude the statement in Ha [write the statement], hence we probably have to tentatively accept the statement in H0 [write the H0 statement].

And accordingly make the business decision; refer to the question for the related business issue on hand.

BUS ADM 216: Dr. Gaurav Bansal