In: Statistics and Probability
1.Suppose that an animal behaviorist is concerned about the effects of a nearby freeway on the nesting behavior of an endangered bird. In this fictional study, suppose that nesting behavior is measured by counting the number of trips to the nest per hour for an individual bird. The animal behaviorist compares a random sample of 40 birds nearby the freeway to a random sample of 40 birds in an undisturbed location. For 24 weeks, the animal behaviorist sets up cameras to count the number of trips to the nest per hour for each bird.
At the end of the 24-week period, the animal behaviorist compares the mean number of trips to the nest per hour for the freeway location and the undisturbed location. The animal behaviorist is using a 5% significance level. The mean number of trips to the nest per hour is less for the birds at the freeway location. The differences are statistically significant at the 4% level.
What conclusion can we draw from these results?
A. The animal behaviorist has proven that nearby freeways cause endangered birds to make less trips per hour to their nests.
B. There is a large difference in the counts of nesting trips for birds in the two groups.
C. There is evidence that nearby freeways may contribute to a change in nesting behavior but the study design prohibits a cause-and-effect conclusion.
D. The sample size is too small to draw a valid conclusion.
2. Weight of a rock: In a geology course, students are learning to use a balance scale to accurately weigh rocks. One student plans to weigh a rock 20 times and then calculate the average of the 20 measurements to estimate her rock's true weight. A second student plans to weigh a rock 5 times and calculate the average of the 5 measurements to estimate his rock's true weight.
The student who weighs his rock 5 times uses the mean to calculate the 95% confidence interval for the rock weight (in grams). His interval is (25.2, 29.1). What does a 95% confidence interval for rock weight tell us in this case?
A.We are 95% confident that this interval includes the mean of the 5 weight measurements taken by this student.
B.We are 95% confident that most rocks of this type weigh between 25.2 g and 29.1 g.
C.We are 95% confident that the true weight of the rock is between 25.2 g and 29.1 g.
3. A medical researcher wants to measure the effects of a new drug on cholesterol levels using a hypothesis test. The target is a 30-point decrease in cholesterol levels after a treatment cycle. The researcher takes a random sample of patients and measures their cholesterol levels before and after a treatment cycle of the drug.
Which type of hypothesis test should they use?
A.test for one population proportion
B.test for one population mean
C.test for a difference in two population proportions
D.test for a difference in two population means
1. Answer-
C is correct option..there is evedence that nearby freeway may contribute to change in nesting behaviour.
This is due to the fact that the difference is statistically significant at 4 % level of significance that means we are 96% sure that the average trip to the best per hour is less than the average that of birds at freeway this suggests that there is slightly change in the behaviour of nesting of undisturbed birds.
2) weight of rock
Answer- C is correct option
As the interval of students who weigh rock five times is between (25.9,29.1) this means that there is 95 % chance that the true weight of the rock must be lie in between the two interval i.e. between 25.9 to 29.1
3 ) B option is correct.
As here the researcher is taking random sample of patients and measure the cholesterol level before and after the treatment cycle of drug.here the population will remains same for the bother sample i.e. before treatment or after treatment so, here is the case of testing of paired means .so here population is one..