a survey of a random sample of 210 male teens and 228 female teens, ages 13 years to 17 years, found that 122 of the male teens and 160 of the female teens brush their teeth at least twice a day. if there is no difference between the proportions in the population of all male and female teens ages 13 years to 17 years who brush their teeth at least twice a day, approximately how many males and females in the sample would be expected to brush their teeth at least twice a day?
If there is no difference between the proportions in the population of all male and female teens ages 13 years to 17 years who brush their teeth at least twice a day, approximately how many males and females in the sample would be expected to brush their teeth at least twice a day?
Answer:
To calculate the expected number of males and females in the sample who would brush their teeth at least twice a day, we first need to find the overall proportion of all teens (males and females combined) who brush their teeth at least twice a day.
Total male teens = 210
Number of male teens who brush their teeth at least twice a day = 122
Overall proportion of males who brush their teeth at least twice a day = \frac{122}{210}
Total female teens = 228
Number of female teens who brush their teeth at least twice a day = 160
Overall proportion of females who brush their teeth at least twice a day = \frac{160}{228}
Since there is no difference between the proportions in the population, we can calculate the overall proportion by combining the data:
Total number of teens = 210 (males) + 228 (females) = 438
Total number of teens who brush their teeth at least twice a day = 122 (males) + 160 (females) = 282
Overall proportion of all teens brushing teeth at least twice a day = \frac{282}{438}
Now, to find the expected number of males and females in the sample who would brush their teeth at least twice a day, we multiply the overall proportion by the total number of males and females:
Expected number of males = \frac{282}{438} \times 210
Expected number of females = \frac{282}{438} \times 228
Calculating these values gives us the approximate expected number of males and females in the sample who would be expected to brush their teeth at least twice a day.