It is necessary to check whether the population is approximately normal because the validity of confidence intervals and hypothesis tests relies on the assumption of normality, particularly when the sample size is small (usually n < 30). If the population distribution is not normal, the sampling distribution of the sample mean may not be normally distributed, leading to inaccurate estimates of the confidence interval and potentially misleading conclusions. When the sample size is larger, the Central Limit Theorem states that the sampling distribution will tend to be normal regardless of the population's distribution, but for smaller samples, a departure from normality can significantly affect results. Therefore, assessing normality helps ensure that the inferences drawn from the sample data are reliable.
The Standard and Poor's (S&P) 500 is a group of 500 large companies traded on the New York Stock Exchange. Following are prices, in dollars, for one day for a random sample of eight stocks.
74.23
35.25
13.19
53.55
84.25
201.94
24.68
53.47
Assume the population standard deviation is o=52
(a) Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.
It is necessary to check whether the population is approximately normal because [blank].
1 answer