HYPOTHESIS TESTING

Fall 2013Nov 14/15

HYPOTHESIS TESTING

•Test assumptions about population parameters using a sample.

•Example: The mean age of targeting consumers is believed to be 35 years old. Conduct a random survey and it returns a sample mean of age 33.

•Question: Should this information change the belief about consumers’ mean age?

STEPS OF HYPOTHESIS TESTING Step 1. State the hypotheses: a pair of mutually exclusive and collectively exhaustive statements about the population parameter.

: Null Hypothesis

: Alternative Hypothesis

Step 2. Select a level of significance.

Most common levels of significance (α) are 10%, 5% and 1%.

STEPS OF HYPOTHESIS TESTING Step 3. Identify the test statistic and its distribution.

For mean:

When population standard deviation is known:

When only sample standard deviation is known:

For proportion:

STEPS OF HYPOTHESIS TESTING Step 4. Decision rule

Critical value method: Compare test statistics with appropriate critical values. If the test statistics fall in the rejection region, reject the null in favor of the alternative. Otherwise fail to reject the null.

P-value method: Compute p-value. If p-value < α , reject the null hypothesis.

•Both methods should yield the same conclusion.

•Never accept the null hypothesis; only fail to reject it.

DECISION RULES-CRITICAL VALUE Two-tailed Test:

Critical Value Critical Value

DECISION RULES-CRITICAL VALUE Left-Tailed Test:

Critical Value

DECISION RULES-CRITICAL VALUE Right-Tailed Test:

Critical Value

CRITICAL VALUES

Test Critical values Excel command

Two-tailed , ,

NORM.S.INV(1-α/2)T.INV(1-α/2, df)

Right-tailed

NORM.S.INV(1-α)T.INV(1-α, df)

Left-tailed NORM.S.INV(α)T.INV(α, df)

P-VALUES

Test P-value Excel command

Left-tailed P() NORM.S.DIST()T.DIST(, df, 1)

Right-tailed

P() 1-NORM.S.DIST(, 1)1-T.DIST(, df, 1)

Two-tailed 2*P() 2*(1-NORM.S.DIST(ABS(), 1))

2*(1-T.DIST(ABS(), df, 1))