# Stats Question

I'm a bit stuck on this question if anyone can help me?

Last year a new mobile phone company, Sonia, produced and stocked shops with 200,000 of their new phone, Sonia 1. The distribution of the battery times is approx- imately normal. Sonia claims that the mean battery time is 16 hours. If the claim is true, which of the following would be more likely? (a) A random sample of 10 phones having a mean battery time greater than 18 hours or (b) A random sample of 50 phones having a mean battery time greater than 18 hours Justify your answer in no more than five sentences.

If the population follows a normal distribution, the sample mean is also normal with the same mean and a variance which is inversely proportional to the sample size. In case of sample (a), the variance would be inversely proportional to 10, while it would be inversely proportional to 50 for sample (b). Thus, sample (a) has greater variance (i.e. deviation from the mean) and would have a higher probability that the mean battery time is greater than 18 hours, as compared to sample (b).
saratirvenracs
01 November 2017
Any of the 2 following statements should be adequate. The a) is more likely to be over 18 hours as small samples are more prone to fall further than the true mean.The higher the number of m. phones the greater the sample. Therefore the closer we are to the true mean.
ron_stats
29 November 2017