Question

How smart is your phone? A random sample of 10 Samsung Galaxy smartphones being sold over the Internet in 2013 had the

following prices, in dollars:
169 385 329 269 149 135
249 349 299 249
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Assume the population standard deviation is σ = 83.
Perform the following.
Part: 0 / 3
Part 1 of 3
(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
(Choose one)

Answer 1

Checking whether the population is approximately normal before constructing a confidence interval is necessary because confidence intervals are based on the assumption that the data follows a normal distribution. If the population is not approximately normal, alternative methods, such as non-parametric tests, may be used.

Step-by-step explanation:

Checking whether the population is approximately normal before constructing a confidence interval is necessary because confidence intervals are based on the assumption that the data follows a normal distribution. When the population distribution is normal, the sampling distribution of the sample mean is also normal, regardless of the sample size. This allows for the use of statistical tests and confidence intervals.

If the population is not approximately normal, the sampling distribution of the sample mean may not be normal, which can lead to inaccurate confidence intervals. In such cases, alternative methods, such as non-parametric tests, may be used. Therefore, it is important to assess the normality of the population before constructing a confidence interval.