Researchers are concerned about the impact of students working they are enrolled
ID: 3227817 • Letter: R
Question
Researchers are concerned about the impact of students working they are enrolled while in classes, and the like to know if students work too much and therefore are spending less time on their classes than they should be. First, the researchers need to find out on the how many hours a week students are working. They know from previous studies that standard deviation this variable about 5 hours. A survey of 200 students provides a sample mean of 7.10 hours worked. What is a 95% confidence interval based on this sample? a) (6.10, 8.10) b (6.41, 7.79) c) (6.57, 7.63) d) (7.10, 8.48) Suppose that this confidence interval was (6 7.38). Which of these is a valid interpretation of this confidence interval? a) There is a 95% probability that the true average number of hours worked by all UF students is between 6.82 and hours. b) There is a 95% probability that a randomly selected student worked between 6.82 and 7.38 hours. c) We are 95% confident that the average number of hours worked by students in our sample is between 6.82 and 7.38 hours. c) We are 95% confident that the average number of hours worked by all UF students is between 6.82 and 7.38 hours. We have 95% confidence in our interval, instead of 100%, because we need to account for the fact that: a) the sample may not be truly random. b) we have a sample, and not the whole population c) the distribution of hours worked may be skewed d) all of the above The researchers are not satisfied with their confidence interval and want to do anotherExplanation / Answer
The formula for 95% confidence interval is given by, (sample mean-1.96.(Sample sd/Square-root(n)), sample mean+1.96.(Sample sd/Square-root(n)))
by using the above formula we can get the right option for question no. 20.
20) sample mean=7.10
sd=5
n=200
Hence the 95% CI is (6.407,7.792)
The correct option is b) (6.41,7.79)
21) a. is the correct option as the probability that the true average number of hours worked by all UF students is between 6.82 and 7.38 hours is .95.
d. is also correct.
22) We have 95% confidence in our interval as the sample may not be random, on the basis of the sample we are trying to draw inference about the entire population, the assuption of testing is the distribution of hours follows normality. Hence the correct answer is option d.
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