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Here is a list hypothesis testing exercises and solutions. Try to solve a question by yourself first before you look at the solution.
Question 1 In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists want to test a new medication to see if it has either a positive or negative effect on intelligence, or not effect at all. A sample of 30 participants who have taken the medication has a mean of 140. Did the medication affect intelligence? View Solution to Question 1
A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 70 on the test. The six students get the following scores:62, 92, 75, 68, 83, 95. Can the professor have 90% confidence that the mean score for the class on the test would be above 70. Solution to Question 2
Question 3 In a packaging plant, a machine packs cartons with jars. It is supposed that a new machine would pack faster on the average than the machine currently used. To test the hypothesis, the time it takes each machine to pack ten cartons are recorded. The result in seconds is as follows.
 42.1 |  42.7 |
 41 |  43.6 |
 41.3 |  43.8 |
 41.8 |  43.3 |
 42.4 |  42.5 |
 42.8 |  43.5 |
 43.2 |  43.1 |
 42.3 |  41.7 |
 41.8 |  44 |
 42.7 | 44.1 |
Do the data provide sufficient evidence to conclude that, on the average, the new machine packs faster? Perform the required hypothesis test at the 5% level of significance. Solution to Question 3Â
Question 4 We want to compare the heights in inches of two groups of individuals. Here are the measurements: X: 175, 168, 168, 190, 156, 181, 182, 175, 174, 179 Y:Â 120, 180, 125, 188, 130, 190, 110, 185, 112, 188 Solution to Question 4Â
Question 5 A clinic provides a program to help their clients lose weight and asks a consumer agency to investigate the effectiveness of the program. The agency takes a sample of 15 people, weighing each person in the sample before the program begins and 3 months later. The results a tabulated below
Determine is the program is effective. Solution to Question 5
Question 6 A sample of 20 students were selected and given a diagnostic module prior to studying for a test. And then they were given the test again after completing the module. . The result of the students scores in the test before and after the test is tabulated below.
We want to see if there is significant improvement in the student’s performance due to this teaching method Solution to Question 6Â
Question 7 A study was performed to test wether cars get better mileage on premium gas than on regular gas. Each of 10 cars was first filled with regular or premium gas, decided by a coin toss, and the mileage for the tank was recorded. The mileage was recorded again for the same cars using other kind of gasoline. Determine wether cars get significantly better mileage with premium gas.
Mileage with regular gas: 16,20,21,22,23,22,27,25,27,28 Mileage with premium gas: 19, 22,24,24,25,25,26,26,28,32 Solution to Question 7Â
Question 8 An automatic cutter machine must cut steel strips of 1200 mm length. From a preliminary data, we checked that the lengths of the pieces produced by the machine can be considered as normal random variables with a 3mm standard deviation. We want to make sure that the machine is set correctly. Therefore 16 pieces of the products are randomly selected and weight. The figures were in mm: 1193,1196,1198,1195,1198,1199,1204,1193,1203,1201,1196,1200,1191,1196,1198,1191 Examine wether there is any significant deviation from the required size Solution to Question 8
Question 9 Blood pressure reading of ten patients before and after medication for reducing the blood pressure are as follows
Patient: 1,2,3,4,5,6,7,8,9,10 Before treatment: 86,84,78,90,92,77,89,90,90,86 After treatment:Â Â Â 80,80,92,79,92,82,88,89,92,83
Test the null hypothesis of no effect agains the alternate hypothesis that medication is effective. Execute it with Wilcoxon test Solution to Question 9
Question on ANOVA Sussan Sound predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all. She randomly divides 24 students into three groups of 8 each. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with nose that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. Their scores are tabulated below.
Group1: Constant sound: 7,4,6,8,6,6,2,9 Group 2: Random sound: 5,5,3,4,4,7,2,2 Group 3: No sound at all: 2,4,7,1,2,1,5,5 Solution to Question 10
Question 11 Using the following three groups of data, perform a one-way analysis of variance using α = 0.05.
51 | 23 | 56 |
45 | 43 | 76 |
33 | 23 | 74 |
45 | 43 | 87 |
67 | 45 | 56 |
Solution to Question 11
Question 12 In a packaging plant, a machine packs cartons with jars. It is supposed that a new machine would pack faster on the average than the machine currently used. To test the hypothesis, the time it takes each machine to pack ten cartons are recorded. The result in seconds is as follows.
New Machine: 42,41,41.3,41.8,42.4,42.8,43.2,42.3,41.8,42.7 Old Machine:Â 42.7,43.6,43.8,43.3,42.5,43.5,43.1,41.7,44,44.1
Perform an F-test to determine if the null hypothesis should be accepted. Solution to Question 12
Question 13 A random sample 500 U.S adults are questioned about their political affiliation and opinion on a tax reform bill. We need to test if the political affiliation and their opinon on a tax reform bill are dependent, at 5% level of significance. The observed contingency table is given below.
total | ||||
138 | 83 | 64 | 285 | |
64 | 67 | 84 | 215 | |
total | 202 | 150 | 148 | 500 |
Solution to Question 13
Question 14 Can a dice be considered regular which is showing the following frequency distribution during 1000 throws?
1 | 2 | 3 | 4 | 5 | 6 | |
182 | 154 | 162 | 175 | 151 | 176 |
Solution to Question 14
Solution to Question 15
Question 16 A newly developed muesli contains five types of seeds (A, B, C, D and E). The percentage of which is 35%, 25%, 20%, 10% and 10% according to the product information. In a randomly selected muesli, the following volume distribution was found.
Component | A | B | C | D | E |
Number of Pieces | 184 | 145 | 100 | 63 | 63 |
Lets us decide about the null hypothesis whether the composition of the sample corresponds to the distribution indicated on the packaging at alpha = 0.1 significance level. Solution to Question 16
Question 17 A research team investigated whether there was any significant correlation between the severity of a certain disease runoff and the age of the patients. During the study, data for n = 200 patients were collected and grouped according to the severity of the disease and the age of the patient. The table below shows the result
41 | 34 | 9 | ||
25 | 25 | 12 | ||
6 | 33 | 15 |
Let us decided about the correlation between the age of the patients and the severity of disease progression. Solution to Question 17
Question 18 A publisher is interested in determine which of three book cover is most attractive. He interviews 400 people in each of the three states (California, Illinois and New York), and asks each person which of the cover he or she prefers. The number of preference for each cover is as follows:
81 | 60 | 182 | 323 | |
78 | 93 | 95 | 266 | |
241 | 247 | 123 | 611 | |
400 | 400 | 400 | 1200 |
Do these data indicate that there are regional differences in people’s preferences concerning these covers? Use the 0.05 level of significance. Solution to Question 18
Question 19 Trees planted along the road were checked for which ones are healthy(H) or diseased (D) and the following arrangement of the trees were obtained:
H H H H D D D H H H H H H H D D H H D D D
Test at the  = 0.05 significance wether this arrangement may be regarded as random
Solution to Question 19Â
Question 20 Suppose we flip a coin n = 15 times and come up with the following arrangements
H T T T H H T T T T H H T H H
(H = head, T = tail)
Test at the alpha = 0.05 significance level whether this arrangement may be regarded as random.
Solution to Question 20
You might also like, how to perform mann-witney u test(step by step) – hypothesis testing, question 13 – chi-square test for independence step by step procedure(political affiliation…), parametric tests in statistics – how to know which to use.
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Below are given the gain in weights (in lbs.) of pigs fed on two diet A and B Dieta 25 32 30 34 24 14 32 24 30 31 35 25 – – DietB 44 34 22 10 47 31 40 30 32 35 18 21 35 29
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Present the findings in your results and discussion section. Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps. Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test.
Hypothesis testing in statistics uses sample data to infer the properties of a whole population. These tests determine whether a random sample provides sufficient evidence to conclude an effect or relationship exists in the population. Researchers use them to help separate genuine population-level effects from false effects that random chance ...
If the biologist set her significance level \(\alpha\) at 0.05 and used the critical value approach to conduct her hypothesis test, she would reject the null hypothesis if her test statistic t* were less than -1.6939 (determined using statistical software or a t-table):s-3-3. Since the biologist's test statistic, t* = -4.60, is less than -1.6939, the biologist rejects the null hypothesis.
State and check the assumptions for a hypothesis test. A random sample of size n is taken. The population standard derivation is known. The sample size is at least 30 or the population of the random variable is normally distributed. Find the sample statistic, test statistic, and p-value. Conclusion; Interpretation; Solution. 1. x = life of battery
Likelihood ratio. In the likelihood ratio test, we reject the null hypothesis if the ratio is above a certain value i.e, reject the null hypothesis if L(X) > đ, else accept it. đ is called the critical ratio.. So this is how we can draw a decision boundary: we separate the observations for which the likelihood ratio is greater than the critical ratio from the observations for which it ...
Hypothesis testing is a crucial procedure to perform when you want to make inferences about a population using a random sample. These inferences include estimating population properties such as the mean, differences between means, proportions, and the relationships between variables. This post provides an overview of statistical hypothesis testing.
Hypothesis testing is a method of statistical inference that considers the null hypothesis H â vs. the alternative hypothesis H a, where we are typically looking to assess evidence against H â. Such a test is used to compare data sets against one another, or compare a data set against some external standard. The former being a two sample ...
In hypothesis testing, the goal is to see if there is sufficient statistical evidence to reject a presumed null hypothesis in favor of a conjectured alternative hypothesis.The null hypothesis is usually denoted \(H_0\) while the alternative hypothesis is usually denoted \(H_1\). An hypothesis test is a statistical decision; the conclusion will either be to reject the null hypothesis in favor ...
What is Hypothesis Testing? In simple terms, hypothesis testing is a method used to make decisions or inferences about population parameters based on sample data. Imagine being handed a dice and asked if it's biased. By rolling it a few times and analyzing the outcomes, you'd be engaging in the essence of hypothesis testing. Think of ...
The specific group being studied. The predicted outcome of the experiment or analysis. 5. Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in ifâŠthen form. The first part of the sentence states the independent variable and the second part states the dependent variable.
In statistics, hypothesis tests are used to test whether or not some hypothesis about a population parameter is true. To perform a hypothesis test in the real world, researchers will obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:. Null Hypothesis (H 0): The sample data occurs purely from chance.
6a.1 - Introduction to Hypothesis Testing ; 6a.2 - Steps for Hypothesis Tests; 6a.3 - Set-Up for One-Sample Hypotheses; 6a.4 - Hypothesis Test for One-Sample Proportion. 6a.4.1 - Making a Decision; 6a.4.2 - More on the P-Value and Rejection Region Approach; 6a.4.3 - Steps in Conducting a Hypothesis Test for \(p\) 6a.5 - Relating the CI to a Two ...
The null hypothesis, denoted as H 0, is the hypothesis that the sample data occurs purely from chance. The alternative hypothesis, denoted as H 1 or H a, is the hypothesis that the sample data is influenced by some non-random cause. Hypothesis Tests. A hypothesis test consists of five steps: 1. State the hypotheses. State the null and ...
A hypothesis test can be used to do this. A hypothesis test involves collecting data from a sample and evaluating the data. Then the statistician makes a decision as to whether or not there is sufficient evidence to reject the null hypothesis based upon analyses of the data. In this section, you will conduct hypothesis tests on single means ...
23.1 How Hypothesis Tests Are Reported in the News 1. Determine the null hypothesis and the alternative hypothesis. 2. Collect and summarize the data into a test statistic. 3. Use the test statistic to determine the p-value. 4. The result is statistically significant if the p-value is less than or equal to the level of significance.
Introduction. Understanding the relationship between sampling distributions, probability distributions, and hypothesis testing is the crucial concept in the NHST â Null Hypothesis Significance Testing â approach to inferential statistics. is crucial, and many introductory text books are excellent here. I will add some here to their discussion, perhaps with a different approach, but the ...
Hypothesis Testing Examples (One Sample Z Test) The one sample z test isn't used very often (because we rarely know the actual population standard deviation). However, it's a good idea to understand how it works as it's one of the simplest tests you can perform in hypothesis testing. In English class you got to learn the basics (like ...
A z test is a way of hypothesis testing that is used for a large sample size (n â„ 30). It is used to determine whether there is a difference between the population mean and the sample mean when the population standard deviation is known.
Hypothesis Testing. Investigators conducting studies need research questions and hypotheses to guide analyses. Starting with broad research questions (RQs), investigators then identify a gap in current clinical practice or research. ... With very large sample sizes, the p-value can be very low significant differences in the reduction of ...
In hypothesis testing, an analyst tests a statistical sample, intending to provide evidence on the plausibility of the null hypothesis. Statistical analysts measure and examine a random sample of ...
Data from a sample is used in hypothesis testing to examine a given hypothesis. We must have a postulated parameter to conduct hypothesis testing. Bootstrap distributions and randomization distributions are created using comparable simulation techniques. The observed sample statistic is the focal point of a bootstrap distribution, whereas the ...
Hypothesis testing is a procedure, based on sample evidence and probability, used to test claims regarding a characteristic of a population. A hypothesis is a claim or statement about a characteristic of a population of interest to us. A hypothesis test is a way for us to use our sample statistics to test a specific claim.
A sample of 20 students were selected and given a diagnostic module prior to studying for a test. And then they were given the test again after completing the module. . ... To test the hypothesis, the time it takes each machine to pack ten cartons are recorded. The result in seconds is as follows. New Machine: 42,41,41.3,41.8,42.4,42.8,43.2,42. ...
Module 5 and 6 homework questions 4. Consider the following hypothesis test. Ho: ”1- ”2 = 0 Ha: ”1- ”2 â 0 The following results are from independent samples taken from two populations. Sample 1 Sample 2 N 35 40 X bar 13.6 10.1 S 5.6 8.7 a. What is the value of the test statistic (to 2 decimals)?
Illustration of the Kolmogorov-Smirnov statistic. The red line is a model CDF, the blue line is an empirical CDF, and the black arrow is the KS statistic.. Kolmogorov-Smirnov test (K-S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions that can be used to test whether a sample came from a ...
Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are: H0: Ëx = 4.5, Ha: Ëx> 4.5 H 0: x ÂŻ = 4.5, H a: x ÂŻ> 4.5.