(a) A study of 35 gamers showed that their average score on a particular game was 90 and the population standard deviation is 5.
(i) Find the best point estimate of the population mean.
(ii) Find the 95% confidence interval of the mean score for all gamers.
(iii) Find the 95% confidence interval of the mean score if a sample of 70 gamers is used instead of a sample of 35.
(iv) From your answer in part (ii) and (iii), which interval is smaller?
(i) The best point estimate for the population mean is the sample mean:
(ii) The critical value for is
The corresponding confidence interval is computed as shown below:
Therefore, based on the data provided, the 95% confidence interval for the population mean is which indicates that we are 95% confident that the true population mean
is contained by the interval
(iii) The critical value for is
The corresponding confidence interval is computed as shown below:
Therefore, based on the data provided, the 95% confidence interval for the population mean is which indicates that we are 95% confident that the true population mean
is contained by the interval
(iv) The 95% confidence interval for is narrower than the 95% confidence interval for
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