Testing the Longevity of Light Bulbs
a. Which t-test should be used to compare the data?
b. Perform a t-test. Should the null hypothesis be rejected or retained?
c. Write a conclusion based on the findings.
a. The students should use the one-sample t-test.b. Based on the t-test, we retain the null hypothesis.
c. There is not enough evidence to suggest a significant difference between the average life of the tested bulbs and the claimed life.
Understanding the T-Test for Light Bulb Longevity
Introduction: Many manufacturers claim that their 100-watt light bulbs have a life of 750 hours. Two students tested this claim by examining 10 bulbs and recording their burnout times. The average burnout time was 740 hours, with a standard deviation (S-hat) of 20.
Choosing the Right T-Test:
To compare the average life of the tested light bulbs to the claimed life, the students should use the one-sample t-test. This test is suitable when the population standard deviation is unknown, as in this case.
Performing the T-Test:
The formula for the t-value is:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
By substituting the values, the students calculated a t-value of approximately -1.58.
Interpreting the Results:
Comparing the t-value to the critical value, it was found that the t-value is greater than the critical value. Thus, the null hypothesis is retained, indicating no significant difference between the average life of the tested bulbs and the claimed life.
Conclusion:
Based on the statistical analysis, there is insufficient evidence to support the idea that the average lifespan of the tested light bulbs differs significantly from the manufacturer's claim of 750 hours.