Mathematics

# Hypothesis Testing Step-by-Step

To conduct hypothesis testing:

1.Create null and alternative hypothesis

2.Calculate z or t test statistics

3.Get the critical value from z or t table

4.Compare calculated value from step 2 with critical value from step 3.

1.

“The null hypothesis is denoted by H0, and the alternative hypothesis is denoted by H1.” (Mann, 2010, p.382) The null hypothesis is usually the hypothesis that is assumed to be true to begin with. The meaning of H0 is null and H1 is alternative. The hypothesis must test to find at least one variable must unequal zero to be significant. In statistics the null hypothesis states that a given claim (or statement) about a population parameter is true.

Null: H0, Alternative: H1 (claim)

H1: ><≠   H0: =

One tailed test: <>      Two tailed test: ≠

Left tailed:  H0: =78     H1: <78

2.

μ: average or population mean (usual or hypothesised population mean)

X̄: sample mean

σ: sigma, population standard deviation

n: sample size

z= x̄-μ/n

z= 30.1-293.8/30 =1.59

Rules for z and t, both rules for z, one rule for t:

1. Population standard deviation of population has to be known (σ)
2. Sample size has to be 30 or more (n)

= z test

3.

Alpha: level of significance

Level of confidence: 99% = 1% significance, possibility of error

Level of significance: is allowable error

Level of confidence: 90, 95, 99 (0.10, 0.05, 0.01)

Level of confidence: 1-alpha

Do NOT use sample mean in hypothesis, and must be same number.

Critical value from: Alpha assume 5%

.05/1 = 0.5        1-0.5 = 0.95

Critical value: 1.65

4.

If, calculated value is greater than the critical value we reject the null hypothesis.

If, calculated value is smaller than the critical value we do not reject the null hypothesis.

Critical value: 1.64

Calculated value: 1.59

H0: μ=29   ✗

H1: μ>29   ✓

Do not reject the null claim is wrong, as we do not reject the null there is not statistical evidence to support the claim.

Reference:

Mann, S. P. (2010). Introductory Statistics; International Student Edition. Seventh Edition. India; Delhi.