Question 1

As part of the foraging behavior assessment described in the previous problem, investigators also measured the bill depths of the male and female Downy Woodpeckers. Summary statistics for these measures are given in the table below:  An initial analysis of the data revealed that it was reasonable to assume the bill depths for both sexes are approximately normal.
a)Construct a 95% confidence interval for the difference in bill depths of the males and females.
b)Do the data indicate that the bill depths differ? Justify your answer statistically.

Accepted Answer

The answer of As part of the foraging behavior assessment...

Question 2

In 1992 Hurricane Andrew struck Florida causing widespread devastation. The eye of Hurricane Andrew passed directly over a site where scientists were studying the ecology of white-tailed deer. The deer had been radio-collared prior to Andrew's appearance, and the hurricane provided an opportunity to study the effects of an awesome storm on the deer. The investigators felt that the home ranges of the deer would change, but were unsure of the direction of the change. (The home range is the average area an animal occupies while foraging for food and defending its territory.) Home ranges of animals usually do not change much unless an area is under ecological stress.
The home range data for a random sample of 18 white-tailed radio-collared deer are shown below in Table 1. The raw area of the home range for each of the deer is reported in hectares for the pre-hurricane year of 1992 and the post hurricane year of 1993. (A hectare is a metric unit of area equal to 2.471 acres.)  ​
a)Using graphical display(s) of your choice show that the assumptions necessary for determining any change in the mean home ranges are plausible.
b)Construct a 95% confidence interval for the difference in means of the home ranges from before Andrew to after Andrew.
c)Do the data provide evidence of a change in the size of the home ranges after Hurricane Andrew? Provide statistical justification for your response.

Accepted Answer

The answer of In 1992 Hurricane Andrew struck Florida causing...

Question 3

The home range of an animal is the average area an animal occupies while foraging for food and defending its territory. It is thought that home ranges of animals usually do not change much, except when an area is under ecological stress. As part of a study of white-tailed deer in Florida in 1991 and 1992, deer were radiocollared and their movements followed over the course of a year. The home range data for a random sample of 18 white-tailed deer are shown below in Table 1. The raw area of the home range for each of the deer is reported in hectares for the years 1991 and 1992. (A hectare is a metric unit of area equal to 2.471 acres.) The investigators are interested in determining whether the home range white-tailed deer change over the course of as little time as a year.  ​
a)Using graphical display(s) of your choice show that the assumptions necessary for determining a change in the mean home ranges are plausible.
b)Construct a 95% confidence interval for the difference in means of the home ranges from 1991 to 1992.
c)Do the data provide evidence of a change in the size of the home ranges between 1991 and 1992? Provide statistical justification for y.

Accepted Answer

The answer of The home range of an animal is...

Question 4

A recent paper described an experiment in which 72 students at a university were assigned at random to one of two groups. All students took a class from the same instructor in the same semester. Students were required to report to an assigned room at a set time to fill out a course evaluation. One group of students reported to a room where they were offered a small bar of chocolate as they entered. The other group reported to a different room where they were not offered chocolate. Summary statistics for the overall course evaluation score are given in the accompanying table.  A 95% confidence interval for the mean difference in overall course evaluation score is:

Accepted Answer

The answer of A recent paper described an experiment in...

Question 5

Suppose that you wish to compare two treatments for preventing baldness in men. (The measure of baldness you will use is the mean number of healthy hair follicles per square cm.) In some circumstances, you may be able to randomly assign the treatments to the men, and in some circumstances, you may not be able to randomly assign the treatments to the men. Respond to the following questions in a few sentences.
a)If you are testing the hypothesis that the means are equal for the population, how would your statistical procedures differ, if at all, depending on whether you randomly assigned subjects to treatments or whether you merely observed differences in men who chose one treatment or the other?
b)How would your interpretation of the results differ, if at all, depending on whether you randomly assigned subjects to treatments or whether you merely observed differences in men who chose one treatment or the other?

Accepted Answer

The answer of Suppose that you wish to compare two...

Question 6

In a recent paper, the authors distinguish between spending money on experiences (such as travel) and spending money on material possessions (such as a car). In an experiment to determine if the type of purchase affects how happy people are after the purchase has been made, 155 college students were randomly assigned to one of two groups. The students in the "experiential" group were asked to recall a time when they spent about $250 on an experience. They rated this purchase on three different happiness scales that were then combined into an overall measure of happiness. The students assigned to the "material" group recalled a time that they spent about $250 on an object and rated this purchase in the same manner. The mean happiness score was 5.62 for the experiential group and 5.44 for the material group. ​
Which of the following hypotheses should be tested to determine the author conclusion that, on average, "experiential purchases induced more reported happiness"?
​

Accepted Answer

The answer of In a recent paper, the authors distinguish...

Question 7

Researchers want to check whether women really speak more than men per day. During the day conversations of 873 adults selected randomly were recorded and then analyzed for the number of words. Researchers report that the mean number of words per day for the sample of women was 15,734 and the mean number for the sample of men was 13,813. The resulting data are given in the accompanying table.
 ​
Construct and interpret a 95% confidence interval estimate for the difference in mean number of words per day for women and men.

Accepted Answer

The answer of Researchers want to check whether women really...

Question 8

Researchers assessed the effectiveness of courses on logic and computer thinking for adult residents of the city. 10 adults were tested on the topic of logic and computer thinking before and after the courses, their knowledge was evaluated on a scale of 0 to 20. The resulting data are given in the accompanying table. Assume that the sample of 10 adults is representative of adult residents of the city.  ​ Construct and interpret a 90% confidence interval estimate for the difference in the mean score before and after courses on logic and computer thinking.

Accepted Answer

The answer of Researchers assessed the effectiveness of courses on...

Question 9

Suppose 9 adult smokers were randomly selected. Researchers want to check whether the movie about the dangers of smoking affects the number of cigarettes smoked. The number of cigarettes per day before and after watching the movie was recorded for each smoker from the sample and resulting data are given in the accompanying table.  ​ Select the most appropriate 95% bootstrap confidence interval for a difference in the mean number of cigarettes per day before and after watching the movie for adult smokers and its correct interpretation.

Accepted Answer

The answer of Suppose 9 adult smokers were randomly selected....

Question 10

Suppose 8 adult patients with the same diagnosis were randomly selected. Researchers want to check whether the injected medication will affect the change in body temperature. The patient's body temperature was measured before and after the injected medication and resulting data are given in the accompanying table.  ​ Construct and interpret a 95% confidence interval estimate for the difference in mean temperature before and after the injected medication.

Accepted Answer

The answer of Suppose 8 adult patients with the same...

Question 11

When estimating the difference between two treatment effects, the format of the confidence interval is different from that used to estimate the difference between two population means.

Accepted Answer

The format of the confidence interval for estimating the difference between two treatment effects is essentially the same as that used for estimating the difference between two population means. Both involve calculating the estimated difference, determining the standard error of the difference, and using a critical value from an appropriate distribution (usually the t-distribution) to construct the interval.

Question 12

When a surgeon repairs injuries, sutures (stitched knots) are sometimes used to hold together and stabilize the injured area. If these knots elongate and loosen, the injury may not heal properly. Researchers at the University of California, San Francisco, tied a particular type of knot with two types of suture material, Maxon and Ticron. Suppose that 112 tissue specimens were available and that for each specimen the type of suture material was randomly assigned. The investigators tested the knots to see how much they elongated. For purposes of this exercise, you can assume that it is reasonable to regard the elongation distributions as approximately normal. Which of the following hypotheses should be tested to determine if there is a significant difference in mean elongation between Maxon versus Ticron threads? ​

Accepted Answer

The answer of When a surgeon repairs injuries, sutures (stitched...

Question 13

The Iowa Tests of Basic Skills is a collection of various achievement tests given to students in grades 1 - 8. Student achievement levels are reported on a scale that runs from 0 to 13. The North Snowshoe Community Schools are evaluating their reading program for students whose native language is not English. In one part of the study the reading comprehension of 10 students, randomly selected from a large population of students in the program, take the Reading Comprehension test in third and fourth grade. Their scores for each year, in grade equivalents, are listed below.  "Normal" growth, by definition, is a change of 1.0. Using the data above, test the hypothesis that the difference in means for 3rd and 4th grade students in this program for non-native English speakers is equal to 1.0.

Accepted Answer

The answer of The Iowa Tests of Basic Skills is...

Question 14

The researchers suggested that the time of the second race in karting is less than during the first race because a person remembers the track. Suppose 8 adults were randomly selected. The time spent on the first and second race was recorded for each person from the sample and resulting data are given in the accompanying table.  Do these data support the claim that the mean difference in time spent on the first and second race is greater than zero? Use a randomization test to select the appropriate output for one set of 1000 simulated sample differences in means and carry out a hypothesis test for a difference in means.

Accepted Answer

The answer of The researchers suggested that the time of...

Question 15

A common memory task is the classification of objects into categories. For example, a table is a piece of furniture; a dog is an animal, etc. This classification capability was used in a recent study of divided attention. College Psychology students were randomly selected and randomly assigned to one of two experimental conditions: divided attention and no divided attention. Students in the "divided attention" group were asked to memorize a list of 36 words while simultaneously listening to a tape recorder; students in a control group were told to memorize a list of 36 words and did not listen to a tape recorder. Each student was then asked to classify the 36 words into 6 categories. (There were 6 words in each category.) The distributions of the correct number of recalled words / category were approximately normal in each of the groups, and a summary of the data for the words/category recalled are presented below:  ​
a)Is there evidence that the memory performance differs in the two groups? Test the appropriate hypothesis using α = 0.05.
b)One possible implication of this study is that high school students should not be dividing their attention by listening to music while studying. What results, if any, of this study would support the contention that students should not be dividing their attention?

Accepted Answer

The answer of A common memory task is the classification...

Question 16

Viruses are infectious agents that often cause diseases in plants. Different viruses have different potency levels, and this fact can be used to detect whether a new virus is infecting plants in the field. In a potency comparison experiment, two viruses were placed on a tobacco leaf of 10 randomly selected tobacco plants in a field. The viruses were randomly assigned to one-half of each of the leaves. The table below presents the potency of the viruses, as measured by the number of lesions appearing on the leaf half.  Test the hypothesis that there is no difference in mean number of lesions for Virus X and Virus Y.

Accepted Answer

The answer of Viruses are infectious agents that often cause...

Question 17

An article describes a study of the effectiveness of a fabric device that acts like a support stocking for a weak or damaged heart. In the study, 94 people who consented to treatment were assigned at random to either a standard treatment (S) consisting of drugs or the experimental treatment (E) that consisted of drugs plus surgery to install the stocking. After two years, 36% of the 61 patients receiving the stocking had improved,while 23% of the patients receiving the standard treatment had improved. Which of the following hypotheses should be tested to determine whether the proportion of patients who improve is significantly higher for the experimental treatment than for the standard treatment? ​

Accepted Answer

The answer of An article describes a study of the...

Question 18

Body fat and lean body mass can be estimated in living animals by measuring the total body electrical conductivity (TOBEC). This technique is useful when attempting to determine if "diet drugs" are working on laboratory rats over time--the researchers need not sacrifice the animals to measure the amount of adipose body fat after periods of drug usage. However, the procedure requires that the animal be totally inside the measurement chamber, which is fairly small. Some rats are so big that their tails must be tucked under their bodies before putting them into the measurement chamber. This is causing concern among the researchers, because there is a possibility the tail position might alter the measurements. To see if the TOBEC measurement is altered by the tail position of the rats, an experiment was run on 16 rats ranging in weight from 210 to 505
g.The rats were randomly assigned the order of measurement, with 8 rats measured in the tail-under position first, and 8 rats in the tail-extended position.The data for the body fat measures, and the differences, are presented in the table below.  ​a)Using graphical display(s) of your choice show that the assumptions necessary for the paired t-test are plausible.b)Test the hypothesis that there is no difference between the population mean TOBEC body fat measurements of rats in the tail-under vs.the tail-extended positions.For purposes of the statistics you may assume that these rats are a random sample of laboratory rats.c)Write a short paragraph based on your analysis above, explaining your results for laboratory technicians.Your paragraph should advise them whether or not it is necessary to make sure the tail positions of the rats are the same when replicating the lean mass body measurements during the experiment.

Accepted Answer

The answer of Body fat and lean body mass can...

Question 19

The perception of danger is an important characteristic for survival of animals. In a field experiment in Costa Rica, investigators located and directly approached black iguanas; that is, they walked straight towards them. Two treatments were randomly assigned to the individual iguanas. In one treatment the investigator gazed at the iguana while approaching, "maintaining eye contact." In a second treatment, the investigator did not gaze at the iguana while approaching. The outcome measure was the distance of the investigator from the iguana when it decided to run away. The researchers believe that eye contact is noticed by the iguana, leading to a longer approach distance. Data from this experiment appears in the table below.  ​
a)Using a graphical display of your choosing, assess the assumption that the distributions of approach distances are approximately normal. State your conclusion in a few sentences.
b)Assuming that it is OK to proceed with a two-sample t procedure, determine if there is sufficient evidence to conclude that there is a shorter mean approach distance for the "Eye contact" group.
c)In a few sentences, state any concerns you have about your conclusions in part (b), based on your results from part (a). If you have no concerns, write "No concerns."

Accepted Answer

The answer of The perception of danger is an important...

Question 20

A study is conducted to determine the effect of different doses of a cold medication on reaction times. In a study of 20 participants between 20 and 25 years of age, half were given a single dose of medication and the other half were given two doses. Thirty minutes after dosing, a simple mechanical experiment measured subject reaction time in milliseconds. The results are summarized below.  Calculate the 95% confidence interval for the difference in reaction times for these two groups. Assume that the reaction times are normally-distributed and that the treatments were randomly assigned.

Accepted Answer

The answer of A study is conducted to determine the...

Quiz 13: Asking and Answering Questions About the Difference Between Two Means

When estimating the difference between two treatment effects, the format of the confidence interval is different from that used to estimate the difference between two population means.