Sunday, 11 March 2018

Hypothesis Testing Solved Examples(Questions and Solutions)

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

Question 2
Aprofessor wants to knowif her introductory statistics class has a good grasp of baic math. Six students are chosen at random form the calll an 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 carons are recorded. The result in seconds is as follows.


 New Machine Old Machine
 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 3 


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:  120, 180, 125, 188, 130, 190, 110, 185, 112, 188
Solution to Question 4 


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 6 


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 7 


Question 8 
An automatic cutter machine must cut steel strips of 1200 mm lenght. From a preliminary data, we checked that the lenghts 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 currectly. 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


How to Conduct Wilcoxon Signed Rank Test
Question 9
Blood pressure reading of ten patients before and afer 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:    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.


Group 1Group 2Group 3
512356
454376
332374
454387
674556

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 carons 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:  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.



favorindifferentopposedtotal
democrat1388364285
republican646784215
total202150148500

Solution to Question 13


Question 14
Can a dice be considered regular which is showing the following frequency distribution during 1000 throws?

Thrown Value123456
Frequency182154162175151176

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 saa, the following volume distribution was found.


ComponentABCDE
Number of Pieces1841451006363

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




Age


below 40 40 - 60 above 60
runoff slight 41 34 9
average 25 25 12
serious 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 determing whinf of three book cover is most attractive. He interviews 400 people in each of the three states (Califonia, 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:



Califonia Illinois New York Total
First Cover 81 60 182 323
Second Cover 78 93 95 266
Third Cover 241 247 123 611
Total 400 400 400 1200
Table 1

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 deseased (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  \varepsilon \!  = 0.05 signnificance wether this arrangeemnt may be regarded as random

Solution to Question 19 


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