the manager of a music store surveyed a random sample who shop in the store about their favorite type of music. the table sows the number of customers who selected each type of music
rock| country | jazz | classical | rap | pop |
37 | 27 | 5 | 9 | 12 | 35
based on the information in the tabe which inference about the favorite type of music of all the customers who shop in the music store appears to be valid
F they are certain to select rock or pop music?
G they are less likely to select country or rap music than rock music
H they are more likely to select country music than jazz,classical,or rap
music
J they are certain to select any type of music other than jazz music
To make an inference about the favorite type of music of all the customers who shop in the music store based on the given table, we need to compare the frequencies of each type of music.
F: To determine if the customers are certain to select rock or pop music, we can add up the frequencies for these two categories:
Rock: 37
Pop: 35
Total: 37 + 35 = 72
Since the total number of customers surveyed is not provided, we cannot be certain if all customers would select rock or pop music. Therefore, option F is not a valid inference.
G: To determine if customers are less likely to select country or rap music than rock music, we can compare the frequencies for these categories:
Rock: 37
Country: 27
Rap: 12
Based on the given frequencies, we can infer that customers are less likely to select country or rap music compared to rock music since the frequencies for country and rap are less than that of rock. Therefore, option G is a valid inference.
H: To determine if customers are more likely to select country music than jazz, classical, or rap music, we can compare the frequencies for these categories:
Country: 27
Jazz: 5
Classical: 9
Rap: 12
Based on the given frequencies, we can infer that customers are more likely to select country music compared to jazz, classical, or rap music since the frequency for country is higher than the frequencies for the other categories. Therefore, option H is a valid inference.
J: To determine if customers are certain to select any type of music other than jazz music, we need to analyze the frequencies for all categories except jazz:
Rock: 37
Country: 27
Classical: 9
Rap: 12
Pop: 35
Based on the given frequencies, we cannot infer that customers are certain to select any type of music other than jazz music since there are frequencies for other categories as well. Therefore, option J is not a valid inference.
Thus, the valid inferences based on the given information are options G and H.