Answer :
The mean of the provided sample of battery reserve capacities is 1.683 hours. To assess the claim of the battery company, a hypothesis test based on the sample mean, standard deviation, and sample size can be conducted to find the p-value, which helps determine the plausibility of the claim.
To answer the question regarding the mean of the sample battery reserve capacities, we first add up the provided hours: 1.75, 1.82, 1.58, 1.63, 1.74, 1.95, 1.32, 1.57, 1.42, 2.05. The total is 16.83 hours. To find the sample mean, we divide this total by the number of batteries, which is 10. So, the mean of the sample is 16.83 / 10 = 1.683 hours.
The claim of the battery company regarding the life span of their new battery could be assessed using a hypothesis test. If the class found that the sample mean life span of their randomly selected batteries was 16.7 hours, which is less than the claimed average of 17 hours, we can use this information along with the standard deviation and the sample size to calculate a z-score and subsequently find the p-value (probability) associated with this result. If the p-value is very low (usually less than 5%), the class may have reason to question the claim because such a result would be unlikely if the claim was true.
