(a) Identify the null hypothesis and alternative hypothesis.

Hypothesis:

Hypothesis is an assumption about the parameter of the population which will be made on the limited evidence as the start value to proceed for further investigation, and the assumption may or may not be true.

In testing the hypothesis is of two types. The two types are:

• Null hypothesis (H₀)
• Alternative hypothesis (H_a)

Null and alternative hypotheses:

Null hypothesis:

Null hypothesis is a statement which is tested for statistical significance in the test. The decision criterion indicates whether the null hypothesis will be rejected or not in the favor of alternative hypothesis. In other words it can be said that, the null hypothesis is a statement which indicates the relationship between statistical measurements, distributions or categories. More often, null hypothesis states no significance relationship between variables or populations. But, null does not indicate “0” all the time.

Alternative hypothesis:

Alternative hypothesis is contradictory statement of the null hypothesis.

The manufacturer guarantees that the mean life of a certain type of light bulb is at least 763 hours.

Let μ be the mean life of a certain type of light bulb.

The null and alternative hypotheses are as follows:

H₀: μ ≥ 763

That is, the mean life of a certain type of light bulb is greater than or equal to 763 hours.

H_a: μ < 763

That is, the mean life of a certain type of light bulb is less than 763 hours.