The manufacturer of a certain type of new cell phone battery claims that the average life span of the batteries is 500 charges; that is, the battery can be charged at least 500 times before failing. To investigate the claim, a consumer group will select a random sample of cell phones with the new battery and use the phones through 500 charges of the battery. The proportion of batteries that fail to last through 500 charges will be recorded. The results will be used to construct a 95 percent confidence interval to estimate the proportion of all such batteries that fail to last through 500 charges.

Based on the information given, it should be noted that a 95% confidence means we are at least 95% sure that the true value of proportion will lie in the interval.

What does the confidence level mean?

When we repeat the sampling 100 times and draw a confidence Interval for each one of them, at least 95 confidence intervals will contain the true value of the proportion. This is what we mean by being 95% confident

Also, when we have a random sample of 5. It implies that the condition of randomness is met and they are independent as well. Since the sample size is very small, the condition of a large sample is not satisfied.

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