1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Y_Kistochka [10]
2 years ago
5

A doctor released the results of clinical trials for a vaccine to prevent a particular disease. In these clinical​ trials, 200,0

00 children were randomly divided in two groups. The subjects in group 1​ (the experimental​ group) were given the​ vaccine, while the subjects in group 2​ (the control​ group) were given a placebo. Of the 100,000 children in the experimental​ group, 21 developed the disease. Of the 100,000 children in the control​ group, 30 developed the disease.
a) Does it appear to be the case that the vaccine was effective? Use the α = 0.01 level of significance.
Identify the null and alternative hypotheses for this test.
c) Find the test statistic for this hypothesis test. (Round to two decimal places as needed.)
Mathematics
1 answer:
CaHeK987 [17]2 years ago
6 0

Answer:

1) No, there is  not  enough evidence to support the claim that the vaccine was effective (P-value=0.104) .

The null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0

being the subindex 1 for the experimental group and subindex 2 for the control group.

2) Test statistic z=-1.26

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the vaccine was effective.

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0

The significance level is 0.01.

The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.

p_1=X_1/n_1=21/100000=0.0002

The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.

p_2=X_2/n_2=30/100000=0.0003

The difference between proportions is (p1-p2)=-0.0001.

p_d=p_1-p_2=0.0002-0.0003=-0.0001

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

P-value=P(z

As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is  not  enough evidence to support the claim that the vaccine was effective.

You might be interested in
Alex wrote the equation c=2n. Describe a situation that this equation could represent.
nevsk [136]
There were 2 times as many caps as nails
make an equation

there were c popsicles each child got 2 popsicles, make an equation for how many popsicles to order if there were n children

bob has c shirts
this is 2 times as many children he has. make an equation for how many shirts he has if he has n children
7 0
2 years ago
How do I determine the coefficient?
Advocard [28]

Answer: You determine the coefficient by looking to see if there is a number in front of a variable. If there is a  number in front of the variable, then that is the coefficient. The coefficient is the number, and the variable is the letter.

Step-by-step explanation: Hope this helps

4 0
2 years ago
The graph of y=cos (x+ pi/2) is the graph of the y = cos(x) shifted in which direction?
Mama L [17]

Step-by-step explanation

7 0
3 years ago
Read 2 more answers
What is d if 3= -6/d
Over [174]

Answer:

d = -2

Step-by-step explanation:

d( 3 ) = ( -6 / d )d

3d = -6

(3d)/3 = (-6)/3

d = -2

6 0
3 years ago
Read 2 more answers
Please help!!!!!!!!!!​
posledela

Answer:

C

Step-by-step explanation:

3/4^2 is just 3/4 x 3/4 which is 9/16

5 0
3 years ago
Read 2 more answers
Other questions:
  • Find the measure of angle 1
    13·2 answers
  • What is the measure of the central angle of a circle with radius 30 centimeters that intercepts an 18π centimeters arc?
    15·1 answer
  • What is the answer to<br><br> 7 y = 84
    10·1 answer
  • Rachel works at a store that sells clothing accessories. The supply function
    7·2 answers
  • Who long does it take to drive 150 miles at 45 miles per hour
    6·2 answers
  • 5 (2x-4)-3 (x-2)=4x-2
    12·1 answer
  • The product of 8 and a number algebraic expression
    7·2 answers
  • Please help! Write the slope-intercept form equation of the trend line
    8·1 answer
  • How to solve equations with the substitution method
    14·2 answers
  • Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find Q3.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!