Stats 13, Quiz 1-5
In Japan there is an annual turkey dog eating contest. The number of turkey dogs that contestants eat are normally distributed with a mean of 36 turkey dogs and a standard deviation of 6 turkey dogs. A contestant eats 27 turkey dogs. What is his z-score?
-1.5
A polling agency wants to find out if the proportion of people who vote for candidate X is higher than the proportion who will vote for candidate Y. What statistical method should he use to test this null?
Two-sample test of the proportion
Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test where H0: the food is safe, and HA: the food is not safe. If you are a consumer, which type of error would be the worst one for the inspector to make, a Type I or a Type II error?
Type II
An article in a sociology journal reports a two-tailed p-value of 0.040 for a test of the null hypothesis that there in no difference between the percentage of men and women who endorse marriage outside one's own religion. If the authors had reported a 95% confidence interval in addition to the P value, which of the following would be true?
Based on the P value given above males and females are not similar with respect to their opinions and the CI should not be expected to capture zero.
Here is a contingency or two-way table for those aboard the Titanic, classsified according to class of ticket and whether or not they survived. First Second Third Crew Total Survived 203 118 178 212 711 Died 122 167 528 673 1490 Total 325 285 706 885 2201 Use the data from the table for problems 1-5. What percent of first class passengers survived?
203/325 = 62.5%
Here is a contingency or two-way table for those aboard the Titanic, classsified according to class of ticket and whether or not they survived. First Second Third Crew Total Survived 203 118 178 212 711 Died 122 167 528 673 1490 Total 325 285 706 885 2201 Use the data from the table for problems 1-5. What pecent of those who survived are first class passengers?
203/711 = 28.6%
Here is a contingency or two-way table for those aboard the Titanic, classsified according to class of ticket and whether or not they survived. First Second Third Crew Total Survived 203 118 178 212 711 Died 122 167 528 673 1490 Total 325 285 706 885 2201 Use the data from the table for problems 1-5. Of all those traveling on the Titanic, what percent are first class passengers?
325/2201 = 14.8%
In standardized scores of achievement motivation that are normally distributed, the US group has a mean score of 35 with a standard deviation of 14. Higher scores correspond to more achievement motivation. Shamu scored in the top 20% of the test takers. What was her score?
47
Jim works in the admission office of a major state university in the east coast. He reports that of the 37000 undergraduates who attend this unversity, 47% are male. He then sends an email to every 10th senior and asks them if they plan to go to graduate school and he finds the percentage to be 23%.
47% is a prameter and 23% is a statistic.
Here is a list of the eye color for 80 UCLA students enrolled in a recent statistics course and whether or not a student wears glasses or corrective lens. Lens No Lens Dark-eyed Black 4 2 6 Brown 19 35 54 Light-eyed Blue 8 4 12 Green 2 3 5 Hazel 1 2 3 Use the data from the table to answer questions 6-9. What percent of these students are dark-eyed?
60/80 = 75%
Here is a contingency or two-way table for those aboard the Titanic, classsified according to class of ticket and whether or not they survived. First Second Third Crew Total Survived 203 118 178 212 711 Died 122 167 528 673 1490 Total 325 285 706 885 2201 Use the data from the table for problems 1-5. If you select person aboard the Titanic, what are the chances that that person is a survivor?
711/2201 = 32.3%
Fluorescent light bulbs have lifetimes that follow a normal distribution, with an average life of 1,685 days and a standard deviation of 1,356 hours. In the production process the manufacturer draws random samples of 197 lightbulbs and determines the mean lifetime of the sample. What is the standard deviation of the sampling distribution of this sample mean?
96.611
In a large statistics class, the professor has each student toss a coin 12 times and calculate the proportion of his or her tosses that were tails. The students then report their results, and the professor plots a histogram of these several proportions. Should a Normal model be used to represent the sampling distribution of the proportion of tails?
A Normal model should not be used because the sample size is not large enough to satisfy the success/failure condition. For this sample size, np=6< 10
A psychologist is examining the effect of showing pictures on learning of words by seven-year-olds. The seven-year-olds are randomly assigned to two groups. The experimental group is shown the word along with the picture. The control group is shown only the word. At the end of the experiment, the subjects are given a test on the number of words they get right. This is an example of:
A well-designed experiment
Among first-year students at a certain university, scores on the verbal SAT follow the normal curve. The average is around 500 and the standard deviation is about 100. Which of the following statements is correct?
Andrew's score is the 60th percentile. So we know his score is 525.
Is a person's favorite ice cream flavor (chocolate, vanilla, etc.) a categorical or quantitative variable?
Categorical
Select the appropriate word to identify whether the measurement represents a categorical variable or a quantitative variable: The name brand of the pair of pants a person is wearing.
Categorical
Given a categorical variable with sufficient data, should we use a box plot to display our variable?
False
A psychological test was performed on a group of 100 people using lottery tickets. Every participant was given a lottery ticket, and told that the prize was a free trip to the Bahamas. They were also told that one person had the winning ticket, but he or she didn't know that they had it. The participants were allowed to either exchange their ticket for another person's, or they could keep their original ticket. It had been assumed that 50 percent of the population would exchange their ticket for another one, but 72 of the 100 participants chose to do so. What are the null and alternative hypotheses, and which distribution should you use to test these hypotheses?
H0: p = 0.50, Ha: p ≠ 0.50, distribution = normal
A teacher wants to examine the impact of using technology on teaching microbiology. He teaches two sections of Microbiology; one at eight and one at ten AM on MWF. He randomly assigns one of the classes to teaching with technology. The students in the the technology class get to know that they are part of an experiment and they try really hard to make the class a success. This is an example of
Hawthore effect
For the overall population, the IQ scores follow the normal distribution with mean equal to 100 and variance equal to 225. What is the best answer?
If you pick a person at random, the chance that his IQ falls between 100 to 115 is more than the chance that his IQ falls between 60-85.
The LAPD has been testing a new system of catching speeders on the 405 over the last 10 months. They wanted to see if they really were catching more speeders, so each month they took 20 samples (with replacement) from the tickets issued in this program . Because their sample sizes were always one-fifth of the tickets, they increased in size each month. How did the sampling distribution of the mean change over the 10 months?
It became close to a normal distribution with the mean equal to the population mean.
Which best describes a sampling distribution model of a statistic?
It is a distribution of all the statistics calculated from all possible samples of the same size.
A survey was conducted at a movie theater to determine movie-goers' preference for different popcorn. The results of the survey show that Brand A was preferred by 65% of the people with a margin of error of plus or minus 3 percent. What does the statement "plus or minus three percent" mean?
It would be unlikely to get the observed proportion of 65% unless the actual percentage of people who preferred Brand A is between 62 and 68 percent.
A recent housing survey was conducted to determine the price of a typical home in Glendale, CA. Glendale is mostly middle-class, with one very expensive suburb. The mean price of a house was roughly $650,000. Which of the following statements is most likely to be true?
Most houses in Glendale cost less than $650,000.
In a large, national study, researchers asked seniors how many alcoholic beverages they had drank in the previous week. The distribution of number of drinks was strongly right-skewed. From this we can conclude that
Most people in the sample had fewer than the average number of drinks.
The distribution of the number of hours that college students watch TV per week is unimodal with a mean of 3.7 and a standard deviation of 5. Is it appropriate to use the normal model to approximate the percentage of hours of TV watching within one standard deviation of the mean?
No, it is not appropriate to use the normal model because it is impossible to watch negative hours of TV per week.
Suppose two researchers wanted to determine if aspirin reduced the chance of a heart attack. Researcher 1 studied the medical records of 500 patients. For each patient, he recorded whether the person took aspirin every day and if the person had ever had a heart attack. Then he reported the percentage of heart attacks for the patients who took aspirin every day and for those who did not take aspirin every day. Researcher 2 also studied 500 people. He randomly assigned half of the patients to take aspirin every day and the other half to take a placebo everyday. After a certain length of time, he reported the percentage of heart attacks for the patients who took aspirin every day and for those who did not take aspirin every day. Suppose that both researchers found that there is a statistically significant difference in the heart attack rates for the aspirin users and the non-aspirin users and that aspirin users had a lower rate of heart attacks. Can both researchers conclude that aspirin caused the reduction?
No, only researcher 2 can conclude this
When a test of significance for the null hypothesis, Ho against the alternative, Ha, the p_value is:
The probability of observing a value of the test statistic at least as extreme as that observed in the sample if Ho is true.
Select the appropriate word to identify whether the measurement represents a categorical variable or a quantitative variable: The average number of minutes a person watches television each day.
Quantitative
A researcher is examining the impact of a new method of teaching Farsi. She concludes that the new method is significantly better than the old method, based on a test with alpha = 0.05. (Testing significance at less than 0.05 as rare)
She could have made the same decision at alpha = 0.10.
Shelly is going to flip a coin 50 times and record the proportion of heads. Her friend Sidney is going to flip a coin 20 times and record the proportion of heads. Which person is more likely to get 20% or fewer heads?
Sidney is more likely to get 20% or fewer heads since the smaller the sample size, the greater the variability in results.
They are showing a new movie at a neighboring theatre. You are hired to ask a sample of 200 people whether they liked the movie or not. You should compute and report the percentage of the people who said "Yes". What kind of sampling method do you recommend?
Systematic random sampling
It is believed that 30% of the people in Washington state want cell phone use banned in cafes. The CEO of a major coffehouse chain in Seattle wonders whether the opinion of the people who go to her cafes is different from the overall population. She hires a polling agency to investigate this issue. In a random sample of 1450 individuals, 474 people have the same opinion as the overall population. What is the p-value?
The correct answers are: 0.01271, 0.0254
A random sample of dates taken from headstones at a cemetery in Pleasanton, California, showed an average lifespan of 70 years with a standard deviation of 20 years. Assuming the distribution is unimodal, which of the following is most likely a good description of the distribution? (consider the context in this question)
The distribution is most likely skewed to the left.
For a class project, every student in a statistics class with 90 students takes a random sample of 200 cars parked at UCLA and records the proportion of clean-air vehicles. (Assume that there are well over 2000 cars parked at UCLA on any given day.) Prior evidence collected by the university suggests that the population proportion is about 10%. Imagine looking at the list of 90 sample proportions. Which of the following is true?
The distribution of sample proportions is well approximated by the Normal model, since the sample size of 200 cars is large enough.
Imagine that students find a recent 10 point quiz very easy and almost all do very well. Describe the shape of distribution of scores when you plot the scores on this quiz
The distribution of scores is skewed left since some students did not do well.
As part of an experiment in perception, 160 UCLA psych students completed a task on identifying similar objects. On average, the students spent 8.25 minutes with standard deviation of 2.4 minutes. However, the minimum time was 2.3 minutes and one students worked for almost 60 minutes. What is the best description of the histogram of times that students spent on this task?
The histogram of times could be right skewed, and in the case of any outliers, it is likely that they will be larger than the mean.
Describing Data Suppose that we create a new data set by doubling the highest value in a large data set of positive values. What statement is FALSE about the new data set?
The median and interquartile range both increase.
A UCLA study questioned whether the percentage of physicians who are smokers in China is the same as in the United States. In the United States, it is believed that 3% of physicians smoke. Suppose that the researchers took a random sample of 1000 Chinese physicians and found that 23% of them were smokers. Then which of the following can we conclude: (Ong, Tong, Gan, Hu, Jiang, Yang, Nan, American Journal of Preventive Medicine, July 2007, from a UCLA press release.)
The p-value for a significance test will be much less than 5%.
A researcher is wondering whether a certain medication helps to lower blood pressure. 200 patients with high blood pressure volunteer to participate in the program. They take the medication for six months and record their blood pressure before and after taking the medication. The researcher does the relevant calculations and finds the Z value to be 1.2
The p-value is 0.115 and the medication did not help to lower the blood pressure.
Several researchers have theorised that humans have longer growth spurts when they live in areas that get more sunlight year-round than other areas. They collect data on the heights of teenaged boys from Equitorial Guinea and from Norway. They also collect data on the hours of sunlight per day for the years that the boys were growing. They conclude that sunlight does cause humans to grow taller.
The researchers' conclusions are not correct because this is an observational study and you can't draw causal conclusions from observational studies.
A consulting statistician reported the results from an experiment to the research psychologist, The report stated that on a particular phase of the experiment, a statistical result yielded a p_value = 0.24. Based on this p_value, which of the following conclusions should the psychologist make?
The test was not statistically significant because, if the null hypothesis is true, one could expect to get a test statistic at least as extreme as our observation about 24% of the time.
The boxplots show the weights of married and single men from a representative sample of men in the U.S. These plots are interesting because they help healthcare professionals know whether married men tend to be heavier than single men. Which of the following provides the best comparison of these distributions?
The typical married man is heavier than the typical single man. The amount of variation in both groups is roughly the same, and both groups have a fairly symmetric distributions, with a few outliers at the heavier end.
A histogram of a sample of data shows that the distribution is right-skewed. If the median of the sample is converted to standard units, which of the following is true?
The z-score will be negative.
A set of scores from a vocabulary test given to a large group of international students can be summarized with this five-number summary: {20,35,45,50,60} Determine which of the following statements about the distribution CANNOT be justified.
There are more scores from 35 to 45 than scores from 45 to 50.
At a hospital they have collected data on the weight (in pounds) and ethnic background (African American, Asian American, Latino, White, and Others) of newborns. What is the best answer?
There is one numerical and one categorical variable.
On the planet Tatooine where the annual famous podrace is held, there is an extensive database of race results going back a couple of decades. Among the variables are the order in which the racers finished (1st, 2nd, 3rd, ...), and their species (Human, Tusken Raider, Ewok, Wookiee, ...).
There is one ordinal variable and one categorical variable
An examination of the medical records of more than 250,000 women in the 20-40 year age range indicated that those who were overweight had longer than average labor when their first child was born. The study concluded that above average weight causes women in the 20-40 year age range to have longer labor when delivering their first child. Choose the best answer.
This conclusion is not correct because there are many other factors other than weight that could contribute to long labor.
We want to examine the effectiveness of three programs on the weight loss of men and women in the 40-50 year old age range. 150 men and 150 women participate in the study. Subjects are randomly assigned to the three programs. They spend 3-4 hours in the program per week and they continue the program for six months. Their weight is recorded before and after the program. Choose the best answer.
This is an experimental study because the subjects have been randomly assigned to different treatment groups
A study indicated that elderly people (age 70 and higher) who had pets lived longer and became less depressed than elderly people who did not have pets. The data came from the records of 700 elderly people who went to a local clinic for treatment. Based on pre-existing medical records, 400 had pets and 300 did not. Choose the best answer.
This is an observational study because the data are obtained from the pre-exisitng medical records of the patients who refer to the local clinic.
Records at a large university (not UCLA, of course) indicate that 20% of all freshmen are placed on academic probation at the end of the first semester. A random sample of 100 freshmen found that 25% of them were placed on probation. The results of the sample: (Note: You May use the Java Applet to get the answer)
are not surprising since the standard deviation of the sampling distribution is 4%.
Based on past experience, a bank believes that 4% of the people who receive loans will not make payments on time. The bank has recently approved 300 loans. What is the probability that over 6% of these clients will not make timely payments? (You May use the Java Applet to get the answer)
between 0.038 and 0.055
Scientists are interested in the effects of the sun on growth of moss on trees above the Arctic Circle. 25 years of data is collected and then analyzed. The study shows that the moss grows the most in the years where there is a moderate amount of sun during the summer, and the least in the years where the sun is mostly obscured by clouds during the summer. This is an example of an
observational study from which we cannot draw causal conclusions
The Federalist Papers are a collection of essays written anonymously by some of the Founding Fathers after the American Revolution to try and convince the 13 states to form a federal government. Although we know who the authors are, we aren't sure who wrote which essay. Essay 28 may have been written by Alexander Hamilton or by James Madison. A historian has noticed that in the essays known to be written by Hamilton that are also around 200 sentences long, the average number of sentences started with a preposition are 68. Around 200 sentences were analysed from Essay 28. The historian finds that about 70 sentences start with a preposition, with a standard deviation of 14 sentences. He conducts a test of the hypothesis Ho:μ=68 against Ha:μ≠68. What is his p-value, and what conclusion can he draw from it?
p.value = 0.043. He should reject the null hypothesis, and conclude that James Madison wrote the essay.
Given the following variables: age in years annual income in dollars gender political affiliation (democrat, republican, independent) You need to use the variables as they are. You cannot transform quantitative data to categories. What would be the best method for studying the relationship between gender and political affiliation and the relationship between gender and annual income?
use a side-by-side boxplot to examine the relationship between gender and annual income and segmented bar chart to examine the relationship between gender and political affiliation.