The mean of a data set is observed to be very different from its median, representing a strong skewness. However, the 1.5 IQR rule reveals t

Question

The mean of a data set is observed to be very different from its median, representing a strong skewness. However, the 1.5 IQR rule reveals that there are no outliers. Which of the following is correct, if the sample size is 100?

a. A normal quantile plot of the data follows a diagonal line, and the t-procedure is appropriate to use.
b. A normal quantile plot of the data does not follow a diagonal line, and the t- procedure is not appropriate to use.
c. A normal quantile plot of the data follows a diagonal line, and the t-procedure is not appropriate to use.
d. A normal quantile plot of the data does not follow a diagonal line, and the t- procedure is appropriate to use.

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Thanh Thu 4 years 2021-07-25T17:55:57+00:00 1 Answers 25 views 0

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  1. Amity
    0
    2021-07-25T17:57:07+00:00
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    Answer:

    a. A normal quantile plot of the data follows a diagonal line, and the t-procedure is appropriate to use.

    Step-by-step explanation:

    Central Limit Theorem

    The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

    For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

    For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

    In this question:

    Sample size of 100 > 30, which means that we use the Central Limit Theorem, and thus, the sampling distribution is approximately normal, following a diagonal line, and since the standard deviation of the population is not know, we use the t-procedure. Thus, the correct answer is given by option a.

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