Write the null and alternative hypotheses. Justify which is the claim. A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is less than 900 hours
The claim: mean < 900
other option: mean > or = 900
The null hypothesis is the one with an equal sign...
Your null hypothesis would be mean=900
Your alt. hypothesis would be mean<900
The alt. hypothesis is the claim.
To write the null and alternative hypotheses for this scenario, let's define a few variables:
Let μ represent the population mean life of the certain type of light bulb.
The null hypothesis, denoted as H0, is a statement that assumes there is no significant difference or effect. In this case, the null hypothesis can be written as:
H0: μ ≥ 900
The alternative hypothesis, denoted as Ha or H1, is a statement that contradicts the null hypothesis and suggests that there is a significant difference or effect. Since the light bulb manufacturer guarantees that the mean life is less than 900 hours, the alternative hypothesis can be written as:
Ha: μ < 900
The claim in this scenario is that the mean life of the certain type of light bulb is less than 900 hours. This aligns with the alternative hypothesis (Ha: μ < 900).