Use the Traditional Method to Test the Given Hypothesis $$\begin{array} { l l l l l l l } 115 & 128 & 107 & 109 & 116 & 124 & 135 \\127 & 115 & 104 & 118 & 126 & 129 & 133\end{array}$$

question 60

Essay

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. For randomly selected adults, IQ scores are normally distributed with a standard deviation of 15. The scores of 14 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of IQ scores of college students is less than 15. Round the sample standard deviation to three decimal places. $$\begin{array} { l l l l l l l } 115 & 128 & 107 & 109 & 116 & 124 & 135 \\127 & 115 & 104 & 118 & 126 & 129 & 133\end{array}$$

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Definitions:

IQR

Short for Interquartile Range, it measures the middle 50% of data points in a dataset, offering a glimpse into data spread.

Range

The difference between the highest and lowest values in a set of data.

Median

The median is the value that lies at the center of a dataset when it is organized in ascending or descending order, splitting the set into two equal parts.

Standard Deviation

A metric that gauges the spread or deviation of a dataset in relation to its average, showing the extent to which the data points are scattered.