# One Tailed Test

#### Case 1

The nule hypothesis is of the type

**H _{0}: μ ≤ μ_{0}**

**H _{0}: p ≤ p_{0}**

The alternative hypothesis, therefore, is of the type

**H _{1}: μ > μ_{0}**

**H _{1}: p >**

**p**

_{0}

### Critical Values

1 - α | α | z_{α} |
---|---|---|

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:

**H _{0} : p ≥ 0.40 ** The absenteeism will be a minimum of 40%.

**H _{1} : 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: z_{α} = 2.33.

Determine the confidence interval:

3. Verify:

4. Decide:

The nule hypothesis, H_{0}, 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

**H _{0}: μ ≤ μ_{0}**

**H _{0}: p ≤ p_{0}**

The alternative hypothesis is, therefore, of type:

**H _{1}: μ > μ_{0}**

**H _{1}: p >**

**p**

_{0}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:

**H _{0} : μ ≤ 120 **

**H _{1} : μ > 120 **

2. Calculate the limit of acceptance:

For a significance level of **α = 0.1**, the corresponding critical value is: z_{α} = 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, H _{0},** cannot be accepted with a significance level equal to 0.1.