a light bulb manufacture claims that the mean life of a certain type of light bulb is more than 750 hours
And you question? Is "college" really the subject ?
To determine if the claim made by the light bulb manufacturer is true, we can conduct a hypothesis test.
Here's how you can go about it:
Step 1: Define the hypotheses:
Null hypothesis (H0): The mean life of the light bulb is 750 hours.
Alternative hypothesis (Ha): The mean life of the light bulb is more than 750 hours.
Step 2: Collect sample data:
Randomly select a sample of light bulbs from the manufacturer's production line. Let's say the sample mean is x̄.
Step 3: Determine the significance level:
Choose a significance level (α), such as 0.05 or 0.01. This denotes the probability of rejecting the null hypothesis when it is true, also known as the Type I error.
Step 4: Compute the test statistic:
Calculate the test statistic based on the sample mean, sample standard deviation (s), sample size (n), and the null hypothesis. In this case, you will use a one-sample t-test because the population standard deviation is unknown. The formula for the test statistic is: t = (x̄ - μ) / (s / √n), where μ is the mean from the null hypothesis.
Step 5: Determine the critical value:
Using the significance level and the degrees of freedom (n-1), find the critical value from the t-distribution table or a statistical software.
Step 6: Compare the test statistic with the critical value:
If the test statistic is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
Step 7: Draw conclusions:
If the null hypothesis is rejected, it suggests evidence to support the claim that the mean life of the light bulb is more than 750 hours. If the null hypothesis is not rejected, there is not enough evidence to support the claim, and the mean life may not be significantly different from 750 hours.
Note: It is important to remember that hypothesis testing is just a statistical inference and cannot provide definitive proof. Statistical significance does not guarantee practical significance.