The University of Southern Mississippi currently uses GE brad fluorescent light bulbs that have a mean life of 900 hours. Sylvania clams that its new fluorescent bulbs, that cost the same as the GE bulbs, last longer than the GE brand. A sample of 50 Sylvania bulbs produces a sample mean of 940 significance level to support Sylvania's claim?

An estimate of variability (e.g., standard deviation) is needed.

The University of Southern Mississippi currently uses GE brad fluorescent light bulbs that have a mean life of 900 hours. Sylvania clams that its new fluorescent bulbs, that cost the same as the GE bulbs, last longer than the GE brand. A sample of 50 Sylvania bulbs produces a sample mean of 940 hours and a sample standard deviation of 70 hours. Is there enough evidence at the alpha = 0.05 significance level to support Sylvania's claim?

To determine if there is enough evidence to support Sylvania's claim that their bulbs last longer than the GE bulbs, we can conduct a hypothesis test.

Here's how to approach this problem:

1. Define the null hypothesis (H0) and alternative hypothesis (Ha):
- Null hypothesis (H0): The mean lifespan of Sylvania bulbs is the same as the mean lifespan of GE bulbs.
- Alternative hypothesis (Ha): The mean lifespan of Sylvania bulbs is greater than the mean lifespan of GE bulbs.

2. Determine the significance level (α):
- The significance level represents the probability of rejecting the null hypothesis when it is true. Commonly used values for α are 0.05 (5%) and 0.01 (1%).

3. Collect sample data:
- The sample consists of 50 Sylvania bulbs, with a sample mean of 940 hours.

4. Determine the test statistic:
- The appropriate test statistic for this problem is the t-statistic because we are dealing with sample means and have a sample standard deviation.

5. Find the critical value:
- Consult the t-distribution table or a statistical calculator to find the critical value corresponding to the chosen significance level and the degrees of freedom.

6. Calculate the t-statistic:
- Use the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
- In this case, the sample mean is 940 hours, and the population mean is 900 hours (GE bulb mean life).
- The population standard deviation is not provided, so we would typically use the sample standard deviation as an estimate if available.

7. Compare the calculated t-statistic with the critical value:
- If the calculated t-statistic is greater than the critical value, we reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.

8. Evaluate the test statistic and make a conclusion:
- Evaluate the calculated t-statistic in comparison to the critical value:
- If the calculated t-statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to support Sylvania's claim.
- If the calculated t-statistic is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to support Sylvania's claim.

Remember to choose an appropriate significance level (α) before conducting the hypothesis test. Your sample size can also affect the power of the test, so keep that in mind as well.