Quizzes and exercises of hypothesis testing

These quizzes and exercises help us review and practice what we obtained in this chapter. They are presented in "show-hide" form similar to the sections of a web page as we are already familiar. Quizzes are multiple choice questions. After choosing an option, an announcement of result appears. To return back to this page, we click "OK" on the announcement. Of course we can choose again.

In exercises, we are required to calculate a value then fill it in an empty rectangle. Note that in this rectangle, only value is acceptable, its unit is not required. After filling the result, we click on "Answer". If the answer is correct, the border of the rectangle is green and there is green "V" symbol in the adjacent square. If the answer is wrong, the border of the rectangle is red and there is red "X" symbol in the adjacent square. We can erase the answer and retry by clicking on "Retry".

For each exercise, there is a hidden solution. To show this solution, we click on "Solution" tab. But try to solve exercises by ourself, don't abuse these solutions.

Quiz 1

Type I of error is committed when we

Quiz 2

Null hypothesis Ho and alternative hypothesis Ha concern

Quiz 3

The higher significance level `alpha` is

Quiz 4

In a certain case, hypothesis testing can consists of

Quiz 5

An equipment uses only water with temporary hardness not greater than 50 mg/L. To test if water from source S satisfies this condition, the alternative hypothesis is (`H_(wS)` is temporary hardness of water from source S)

Quiz 6

To study the effect of music on memory, we choose 20 students, test their memory before and after listening music. Which type of hypothesis testing should be applied.

Quiz 7

In statistics, hypothesis is a statement concerning

Quiz 8

Percentage point table of chi-square distribution is used when we compare

Quiz 9

In testing the independence of attributes, we have to calculate the square of difference between real values and theoretical ones. These theoretical values are calculated based on:

Quiz 10

In hypothesis testing, value of critical value `t`* depends on

Exercise 1

To evaluate the risk of cardiovascular disease (CVD) in company A, total cholesterol of 12 workers were measured. The result is shown in Table 1.

Table 1 Total cholesterol of workers (in mg/dL)
215	239	162	174	136	185
166	175	194	188	219	182

Assume that total cholesterol is normally distributed.

a. What are the mean and standard deviation of total cholesterol of 12 workers above (in mg/dL).

• Mean :

• Standard deviation :

Quiz b

By health standard, total cholesterol (symbolized as C_chol) lower than 200 mg/dL is considered as safe for CVD. If we would like to test the risk of CVD in whole company A, the alternative hypothesis is

c. What is the value of critical value of `t`* if confidence level is 95%?

d. What is the value of test statistic `t_o`?

Quiz e

We conclude that concerning CVD, the workers of company A are

Solution

a. From Table 1, Mean : 186,25 mg/mL ; standard deviation : 27,90 mg/mL.

b. Hypotheses : Ho : C_{chol, A} = 200 mg/dL (unsafe) ; Ha : C_{chol, A} < 200 mg/dL (safe).

c. Rejection region is in the left of `t`* : `t`*`=t_(0,95,11)`

Using percentage point table of Student's distribution :

`t`*`=t_(0,95,11)=-t_(0,05,11)=-1,7959`

d. From data of Table 1 : `t_o=(bar x-a)/(s/sqrt(n))=(186,25-200)/((27,9028)/sqrt(12))=-1,707`

e. Because `t_o>t`* , we cannot reject Ho : C_{chol, A} = 200 mg/dL.
Workers of company A are unsafe with CVD.

Exercise 2

To compare the participation in sport of students of universities A and B, a survey was conducted with 100 students of university A and 80 students of university B. The result shows that 36 students of university A and 24 students of university B participate frequently in sportive activities.

a. Determine the proportions `p_A` and `p_B` of students of universities A and B participating in sportive activities (in samples).

• `p_A` =

• `p_B` =

Quiz b

To compare these two proportions, alternative hypothesis Ha is

c. What is the common proportion of students participating in sportive activities `p_c` (in two samples)?

• `p_c` =

d. What is the standard deviation `sigma_c` of `p_c`?

• `sigma_c` =

e. What is the critical value `z`*? (confidence level is 95%).

• `z`* =

f. What is the value of test statistic `z_o`?

• `z_o` =

Quiz g

With confidence level 95%, we conclude that the proportion of students participating in sportive activities

Solution

a. `p_A=0,36` ; `p_B=0,30`

b. We recognize `p_A>p_B`. We would like to test if this difference is true. So Ha : `pi_A>pi_B`.

c. `p_c=(36+24)//(100+80)=0,3333`

d. `sigma_c=sqrt(p_cq_c(1/n_1+1/n_2))=sqrt(0,3333xx0,6667(1/100+1/80))=0,0707`

e. Rejection region is in the right of critical value `z`*. Using percentage point table of Student's distribution (the last row):

`z`*`=z_(0,05)=1,6449`

f. `z_o=(p_A-p_B)/sigma_c=(0,36-0,30)/0,0707=0,849`

g. Because `z_o< z`* , we cannot reject Ho (`pi_A=pi_B`).

With confidence level of 95%, we conclude that the proportions of students participating in sportive activities of universities A and B are equal.

This web page was last updated on 03 December 2018.