# One Tailed Test

#### Case 1

The nule hypothesis is of the type H0: μ ≥ k (or H0: p ≥ k).

The alternative hypothesis, therefore, is of the type H1: μ < k (or H1: p < k).

### Critical Values

1 - α α zα
0.90 0.10 1.28
0.95 0.05 1.645
0.99 0.01 2.33

The significance level, α, is concentrated in one part or tail.

The limit of acceptance in this case is:

or:

#### Example

A sociologist has predicted that in a given city, the level of absenteeism in the upcoming elections will be a minimum of 40%. Of a random sample of 200 individuals from the voting population, 75 state they will likely vote. Determine with a significance level of 1%, if the hypothesis can be accepted.

1. State the null and alternative hypotheses:

H0 : p ≥ 0.40      The absenteeism will be a minimum of 40%.

H1 : p < 0.40     The absenteeism will be a maximum of 40%.

2. Calculate the limit of acceptance:

For a significance level of α = 0.01, the corresponding critcal value is: zα = 2.33.

Determine the confidence interval:

3. Verify:

4. Decide:

The nule hypothesis, H0, should be accepted as it can be stated with a confidence level of 1% that absenteeism will be at least 40% for the upcoming election.

#### Case 2

The nule hypothesis is of type H0: μ ≤ k (or H0: p ≤ k).

The alternative hypothesis is, therefore, of type H1: μ > k (or H1: p > k).

The significance level, α, is concentrated in one part or tail.

The limit of acceptance in this case is:

or:

#### Example

A report indicates that the maximum price of a plane ticket between New York and Chicago is \$120 with a standard deviation of \$40. A sample of 100 passengers shows that the average price of their tickets was \$128.

Can the above statement be accepted with a significance level equal to 0.1?

1. State the null and alternative hypotheses:

H0 : μ ≤ 120

H1 : μ > 120

2. Calculate the limit of acceptance:

For a significance level of α = 0.1, the corresponding critical value is: zα = 1.28.

Calculate the confidence interval for the mean:

3. Verify:

The value of the mean of the sample is: \$128.

4. Decide:

The nule hypothesis, H0, cannot be accepted with a significance level equal to 0.1.