Chapters 1-24 Flashcards
An observational study found that the amount of sleep an employee gets each night is associated with job the correlation coefficient was found to be r=.86 A reader of the study concluded that more sleep causes employees to perform better why is such conclusion not correct?
Causation cannot be determined from an observational study
Two voting districts, C and M, were sampled to investigate voter opinion about tax spending. From a random sample of 100 voters in District C, 22 percent responded yes to the question “Are you in favor of an increase in state spending on the arts?” An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question. A 95 percent confidence interval for the difference (Pc - Pm) was calculated as -0.04 (+/-) 0.12. Which of the following is the best interpretation of the interval?
We are 95% confident that the difference in the proportions of all voters in districts C and M who favor an increase in state spending for the arts is between -0.16 and 0.08.
A local arts council has 200 members. The council president wanted to estimate the percent of its members who have had experience in writing grants. The president randomly selected 30 members and surveyed the selected members on their grant-writing experience. Of the 30 selected members, 12 indicated that they did have the experience. Have the conditions for inference with a one-sample z-interval been met?
No, because the sample size is not less than 10 percent of the population size
A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?
Even with a correlation value of 0.94, it is possible the relationship could still be better represented by a nonlinear model.
A factory manager selected a random sample of partes produced on an old assembly line and a random sample of parts produced on a new assembly line. The difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is treated than that of the new assembly line. The P-Value of the test was 0.018. Which of the following is the correct interpretation of the P-Value?
If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing of at least 0.006 is 0.018.
For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?
A random sample of 10 taken from a population distribution that is skewed to the right, because it is skewed, the sample size needs to be at least 30 to assume the normality for the sampling distribution.
According to a recent survey, 31% of the residents of a certain state who are age 25 years or older have a bachelor’s degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability B will equal 40?
B has a binomial distribution, with the probability of success of 0.31 and the probability of failure of 0.69. The probability of 40 out of 50 people having a degree is
(50/40) (0.31)^40 (0.69)^10
A high school science teacher has 78 students, of those students, 35 are in the band and 32 are on a sports team. There are 16 students who are not in the band or on a sports team. One students from the 78 students will be selected at random. Let event B represent the event of selecting a student in the band, and let event S represent the event of selecting a student on a sport team. Are B and S mutually exclusive events?
No, because P(B upside down U S)= 5/78
The sum of 35, 32 and 16 is 83, which is 5 greater than 78. So there must be 5 students who are both in the band and on a sports team, bc both events can occur at the same time, they are not mutually exclusive.
In a population of bats living in a certain region, 30% have a wingspan greater than 10 inches. In a random sample of 80 bats living outside the region, 20 had a wingspan greater than 10 inches . Consider a one-sample z test to investigate whether there is evidence that the proportion of bats with a wingspan greater than 10 inches living outside the region is different from that of the bats living in the region. Which of the following is the correct test statistic?
z= 0.25-0.30/ square root of (0.30)(0.70)/ 50
