A manufacturer claims that the lifetime of a certain brand of batteries produced by his factory has a variance of 500 hours. A sample size 26 has a variance of 7200 hours. Assuming that it is reasonable to treat these data as a random sample from a normal population. Let us manufacturer's claims at 0.02 level of significance.

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Did you know that in statistical analysis, the variance of a sample provides information about the variability or spread of the data? In this case, a manufacturer claims that the lifetime of a specific brand of batteries from his factory has a variance of 500 hours. However, when a sample size of 26 batteries is taken from this factory, it is found that the variance is 7200 hours. By considering this data as a random sample from a normal population, statistical testing can be used to assess the manufacturer's claims. To determine if there is sufficient evidence to reject the claim, a significance level of 0.02 is chosen. This process allows for a rigorous evaluation of the manufacturer's assertions, aiding in informed decision-making.