She sounds tall! Presented with recordings of a pair of people of the same sex s

Question

She sounds tall! Presented with recordings of a pair of people of the same sex speaking the same phrase, can a listener determine which speaker is taller simply from the sound of their voice? Twenty four young adults at Washington University listened to 100 pairs of speakers, and within each pair were asked to indicate which of the two speakers was the taller. Here are the number correct (out of 100) for each of the 24 participants (NOTE: The numerical values in this problem have been modified for testing purposes.) 65 61 67 59 58 62 56 67 61 67 63 54 68 49 66 58 69 70 65 56 68 56 58 72 Researchers believe that the key to correct discrimination is contained in a particular type of sound produced in the lower airways or the lungs, known as subglottal resonances, whose frequency is lower for taller people. Despite the masking of these resonances by other voice sounds, researchers wondered whether the information they contained could still be heard by listeners and used to identify the taller person. (a) Make two stemplots, with and without splitting the stems. 4 5 6 7 4 5 5 6 6 7 (b) The center is about correct identifications. (c) The distribution is somewhat left-skewed right-skewed (d) If the experimental subjects are just guessing which speaker is taller, they should correctly identify the taller person about 50% of the time. Does this data support the researchers, conjecture that there is information in a person's voice to help identify the taller person? No Yes Check Syntax

Explanation / Answer

(a)

WIthout spliting the stem:

With spliting the stem:

(b)

Here we should use median as center. The center is average of 12 th and 13th data values.

12th data value: 62

13th data value: 63

Median: (62+63) /2 = 62.5

(c)

The distribution is skewed to left slightly.

(d)

Yes becuase out of 24 listeners 23 listeners recognize correctly more then 50 pairs.

Stem and Leaf plot for X stem unit = 10 leaf unit = 1 Frequency Stem Leaf 1 4 9 8 5 4 6 6 6 8 8 8 9 13 6 1 1 2 3 5 5 6 7 7 7 8 8 9 2 7 0 2 24

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