Hypothesis Testing Exercises And Solutions Pdf

hypothesis testing exercises and solutions pdf

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To install Python and these dependencies, we recommend that you download Anaconda Python or Enthought Canopy , or preferably use the package manager if you are under Ubuntu or other linux.

Test of a single population mean. H a tells you the test is left-tailed. The picture of the p -value is as follows:. Assume the p -value is 0.

solved problems on hypothesis testing pdf

Use the following information to answer the next three exercises. A grocery store is interested in how much money, on average, their customers spend each visit in the produce department. Identify the population, sample, parameter, statistic, variable, and data for this example.

This is an example of a:. Use the following information to answer the next two exercises. A health club is interested in knowing how many times a typical member uses the club in a week.

They decide to ask every tenth customer on a specified day to complete a short survey including information about how many times they have visited the club in the past week. Describe a situation in which you would calculate a parameter, rather than a statistic.

The U. One question asks whether they are planning to attend a four-year college or university in the following year.

Fifty percent answer yes to this question; that fifty percent is a:. Imagine that the U. This 50 percent is an example of a:. A survey of a random sample of nurses working at a large hospital asked how many years they had been working in the profession. Their answers are summarized in the following incomplete table. Fill in the blanks in the table and round your answers to two decimal places for the Relative Frequency and Cumulative Relative Frequency cells. Describe how you might draw a random sample of 30 students from a lecture class of students.

A manager wants to draw a sample, without replacement, of 30 employees from a workforce of Describe how the chance of being selected will change over the course of drawing the sample. The manager of a department store decides to measure employee satisfaction by selecting four departments at random, and conducting interviews with all the employees in those four departments. What type of survey design is this? A popular American television sports program conducts a poll of viewers to see which team they believe will win the NFL National Football League championship this year.

Viewers vote by calling a number displayed on the television screen and telling the operator which team they think will win. Do you think that those who participate in this poll are representative of all football fans in America? Two researchers studying vaccination rates independently draw samples of 50 children, ages 3—18 months, from a large urban area, and determine if they are up to date on their vaccinations.

One researcher finds that 84 percent of the children in her sample are up to date, and the other finds that 86 percent in his sample are up to date. Assuming both followed proper sampling procedures and did their calculations correctly, what is a likely explanation for this discrepancy? A high school increased the length of the school day from 6.

Students who wished to attend this high school were required to sign contracts pledging to put forth their best effort on their school work and to obey the school rules; if they did not wish to do so, they could attend another high school in the district.

At the end of one year, student performance on statewide tests had increased by ten percentage points over the previous year. Does this improvement prove that a longer school day improves student achievement? You read a newspaper article reporting that eating almonds leads to increased life satisfaction.

The study was conducted by the Almond Growers Association, and was based on a randomized survey asking people about their consumption of various foods, including almonds, and also about their satisfaction with different aspects of their life.

Does anything about this poll lead you to question its conclusion? A psychologist is interested in whether the size of tableware bowls, plates, etc. He randomly assigns college students to one of two groups: the first is served a meal using normal-sized tableware, while the second is served the same meal, but using tableware that it 20 percent smaller than normal. He records how much food is consumed by each group.

Identify the following components of this study. A researcher analyzes the results of the SAT Scholastic Aptitude Test over a five-year period and finds that male students on average score higher on the math section, and female students on average score higher on the verbal section.

She concludes that these observed differences in test performance are due to genetic factors. Explain how lurking variables could offer an alternative explanation for the observed differences in test scores.

Explain why it would not be possible to use random assignment to study the health effects of smoking. What are some sources of bias with this survey? A professor offers extra credit to students who take part in her research studies. What is an ethical problem with this method of recruiting subjects? Use the following information to answer the next four exercises. Do you see any outliers in this data? If so, how would you address the situation? Construct a stem plot for this data, using only the values in the range 0— In a class of 35 students, seven students received scores in the 70—79 range.

What is the relative frequency of scores in this range? You conduct a poll of 30 students to see how many classes they are taking this term. You decide to construct a histogram of this data.

What will be the range of your first bar, and what will be the central point? Which bar in this histogram will be the tallest, and what will be its height?

You get data from the U. Census Bureau on the median household income for your city, and decide to display it graphically. Which is the better choice for this data, a bar graph or a histogram?

You collect data on the color of cars driven by students in your statistics class, and want to display this information graphically. Your daughter brings home test scores showing that she scored in the 80 th percentile in math and the 76 th percentile in reading for her grade.

Interpret these scores. You have to wait 90 minutes in the emergency room of a hospital before you can see a doctor. You learn that your wait time was in the 82 nd percentile of all wait times.

Explain what this means, and whether you think it is good or bad. This box plot represents scores on the final exam for a physics class. In a marathon, the median finishing time was three hours, 35 minutes, and four seconds. You finished in Interpret the meaning of the median time, and discuss your time in relation to it.

The value, in thousands of dollars, for houses on a block, are: 45; 47; Which do you think better reflects the average value of the homes on this block? In a symmetrical distribution what will be the relationship among the mean, median, and mode?

Compute the mean and standard deviation for this data; use the sample formula for the standard deviation. Express the number In a biology class, the scores on the final exam were normally distributed, with a mean of 85, and a standard deviation of five.

Susan got a final exam score of Express her exam result as a z -score, and interpret its meaning. You have a jar full of marbles: 50 are red, 25 are blue, and 15 are yellow. Assume you draw one marble at random for each trial, and replace it before the next trial. Which is more likely, drawing a red marble or a yellow marble?

Justify your answer numerically. The following are probabilities describing a group of college students. Write the symbols for the probability that a student, selected at random, is both female and a science major. Write the symbols for the probability that the student is an education major, given that the student is male. C and D are mutually exclusive events. In a high school graduating class of , students are going to college, 40 are planning to work full-time, and 80 are taking a gap year.

Are these events mutually exclusive? An archer hits the center of the target the bullseye 70 percent of the time. However, she is a streak shooter, and if she hits the center on one shot, her probability of hitting it on the shot immediately following is 0.

Calculate the probability that she will hit the center of the target on two consecutive shots. Are P A and P B independent in this example? The following contingency table displays the number of students who report studying at least 15 hours per week, and how many made the honor roll in the past semester. At a high school, some students play on the tennis team, some play on the soccer team, but neither plays both tennis and soccer.

Draw a Venn diagram illustrating this. At a high school, some students play tennis, some play soccer, and some play both. Sample Answer: Any solution in which you use data from the entire population is acceptable. For instance, a professor might calculate the average exam score for her class: because the scores of all members of the class were used in the calculation, the average is a parameter.

Sample Answer: One possibility is to obtain the class roster and assign each student a number from 1 to Then use a random number generator or table of random number to generate 30 numbers between 1 and , and select the students matching the random numbers. One possibility would be to obtain a roster of students enrolled in the college, including the class standing for each student.

Hypothesis Testing

These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax. Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for. Of interest is whether the proportions are in fact equal. A new laundry detergent is tested on consumers. Of interest is the proportion of consumers who prefer the new brand over the leading competitor. A study is done to test this.

When you are evaluating a hypothesis, you need to account for both the variability in your sample and how large your sample is. Hypothesis testing is generally used when you are comparing two or more groups. For example , you might implement protocols for performing intubation on pediatric patients in the pre-hospital setting. To evaluate whether these protocols were successful in improving intubation rates, you could measure the intubation rate over time in one group randomly assigned to training in the new protocols, and compare this to the intubation rate over time in another control group that did not receive training in the new protocols. Based on this information, you'd like to make an assessment of whether any differences you see are meaningful, or if they are likely just due to chance. This is formally done through a process called hypothesis testing.

testing hypothesis, test statistic, P-value. Text Book: Basic Concepts and Solution. 1-Data: variable is age, n=10, =27,σ2=20,α= 2-Assumptions: the population Exercises Q. Escobar performed a study to validate a translated.

9.E: Hypothesis Testing with One Sample (Exercises)

These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax. Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking.

The random variable is the proportion of people picked at random in Times Square visiting the city. The data do support the claim. Note that here the large-sample 1 — PropZTest provides the approximate p -value of 0.

Ever make bets with your family and friends about sports, singing or dancing competitions? You can think of these bets as a hypothesis. A hypothesis is defined as a proposed explanation for an event based on previous facts.

solved problems on hypothesis testing pdf

Use the following information to answer the next three exercises. A grocery store is interested in how much money, on average, their customers spend each visit in the produce department.

Hypothesis Testing

Significance tests give us a formal process for using sample data to evaluate the likelihood of some claim about a population value. Patients were given exercise tests at baseline and after 6 months of follow up. It's simple: each one of our tutorial videos explains how to answer one of the exam questions provided. Perform a hypothesis test 6 step procedure outlined in class and state your decision. Step 4 Make the decision to reject or not reject the null hypothesis. The mean daily return of the sample is 0.

The previous two chapters treated the questions of estimating and making inferences about a parameter of a single population. In this chapter we consider a comparison of parameters that belong to two different populations. For example, we might wish to compare the average income of all adults in one region of the country with the average income of those in another region, or we might wish to compare the proportion of all men who are vegetarians with the proportion of all women who are vegetarians.

9.E: Hypothesis Testing with One Sample (Exercises)

Hypothesis testing is an important activity of empirical research and evidence-based medicine. A well worked up hypothesis is half the answer to the research question. For this, both knowledge of the subject derived from extensive review of the literature and working knowledge of basic statistical concepts are desirable.

Ever make bets with your family and friends about sports, singing or dancing competitions? You can think of these bets as a hypothesis. A hypothesis is defined as a proposed explanation for an event based on previous facts.

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