In the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:
Ho: mean = 8.0
Ha: mean > 8.0
To perform a hypothesis test to determine whether the mean running time of the flashlight battery has increased as a result of the production method change, we need to set up the null and alternative hypotheses.
The null hypothesis, denoted as H0, assumes no change or no difference in the mean running time after the production method change. In this case, the null hypothesis would be:
H0: The mean running time of the flashlight battery is still 8.0 hours.
The alternative hypothesis, denoted as Ha or H1, asserts the desired change or difference in the mean running time. In this case, the alternative hypothesis would be:
Ha: The mean running time of the flashlight battery has increased after the production method change.
To statistically test these hypotheses, we need to collect a sample of flashlight batteries and measure their running times. Then, we can analyze the sample data using a suitable statistical test, such as a t-test or z-test.
Here are the general steps to perform the hypothesis test:
1. Define the null and alternative hypotheses.
2. Determine the significance level (usually denoted as α) for the test.
3. Collect a random sample of flashlight batteries and measure their running times.
4. Calculate the sample mean and sample standard deviation of the running times.
5. Determine the appropriate test statistic depending on the sample size and whether population standard deviation is known or unknown.
6. Calculate the test statistic using the sample data.
7. Determine the critical value(s) or p-value(s) corresponding to the chosen significance level.
8. Compare the test statistic to the critical value(s) or p-value(s).
9. Make a decision to either reject or fail to reject the null hypothesis based on the comparison.
10. Interpret the results in the context of the problem.
Performing this hypothesis test will help us evaluate whether the production method change has had a significant impact on the mean running time of the flashlight battery.