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) state the individual and variable of interest (is it the listeners??)
b) state 3 graphs you could use for this type of variable (i chose stemplot, bar graph, and boxplot, but which one can help me find the exact value?)
c) is this a normal distribution? (what does this mean?)
a) The individuals of interest in this study are the 24 participants who listened to the recordings. The variable of interest is the number of correct responses (out of 100) made by each participant.
b) To represent this type of variable, you could use the following graphs:
1. Histogram: A histogram can show the distribution of the number of correct responses made by the participants. The x-axis would represent the number of correct responses, and the y-axis would represent the frequency or count of participants.
2. Bar graph: A bar graph can also be used to display the number of correct responses, with the x-axis representing the participants and the y-axis representing the number of correct responses.
3. Box plot: A box plot can provide a visual representation of the distribution of the number of correct responses. It displays the minimum, maximum, median, and quartiles of the data.
Out of the three graph options you mentioned, a box plot would be the most useful for finding the exact values of the number of correct responses. It provides summary statistics that can help identify the spread and central tendency of the data.
c) To determine whether the number of correct responses follows a normal distribution, you would need to analyze the data. A normal distribution refers to a symmetric bell-shaped curve where the data clusters around the mean, following a specific mathematical pattern called the Gaussian distribution.
To assess if the data is normally distributed, you can use techniques like a normal probability plot or statistical tests such as the Shapiro-Wilk test or the Anderson-Darling test. These tests can evaluate if the data significantly deviates from a normal distribution.
a) The individuals of interest in this study are the 24 participants who listened to the recordings. The variable of interest is the number of correct identifications of the taller speaker.
b) Three graphs that could be used for this type of variable are:
1. Stemplot (Stem-and-leaf plot): This graph can show the distribution of the number of correct identifications for each participant.
2. Bar graph (Histogram): This graph can display the frequency or count of participants who achieved different levels of correct identifications.
3. Boxplot (Box-and-whisker plot): This graph can provide a visual summary of the distribution of correct identifications, including measures like the median, quartiles, and outliers. However, it doesn't provide exact values.
c) The given information does not provide data to directly determine whether the distribution of correct identifications is normal or not. Normal distribution refers to a specific type of probability distribution where the data is symmetric around the mean and follows a bell-shaped curve. To determine if the distribution is normal, you would need additional information, such as the actual values of correct identifications for each participant.