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
antoniya [11.8K]
3 years ago
12

Many elementary school students in a school district currently have ear infections. A random sample of children in two different

schools found that 16 of 42 at one school and 18 of 34 at the other have ear infections. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools? Group of answer choices
Mathematics
1 answer:
Marta_Voda [28]3 years ago
5 0

Answer:

Step-by-step explanation:

The summary of the given data includes;

sample size for the first school n_1 = 42

sample size for the second school n_2  = 34

so 16 out of 42 i.e x_1 = 16 and 18 out of 34 i.e x_2 = 18 have ear infection.

the proportion of students with ear infection Is as follows:

\hat p_1 = \dfrac{16}{42} = 0.38095

\hat p_2 = \dfrac{18}{34}  =  0.5294

Since this is a two tailed test , the null and the alternative hypothesis can be computed as :

H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0

level of significance ∝ = 0.05,

Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.

The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.

\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}

\bar p = \dfrac{16 +18}{42 +34}

\bar p = \dfrac{34}{76}

\bar p = 0.447368

\bar p + \bar  q = 1 \\ \\ \bar q = 1 -\bar  p \\  \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632

The pooled standard error can be computed by using the formula:

S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} +  \dfrac{\bar p \bar p}{n_2} }

S.E = \sqrt{ \dfrac{  0.447368 *  0.552632}{ 42} +  \dfrac{ 0.447368 *  0.447368}{34} }

S.E = \sqrt{ \dfrac{  0.2472298726}{ 42} +  \dfrac{ 0.2001381274}{34} }

S.E = \sqrt{ 0.01177284105}

S.E = 0.1085

The test statistics is ;

z = \dfrac{\hat p_1 - \hat p_2}{S.E}

z = \dfrac{0.38095- 0.5294}{0.1085}

z = \dfrac{-0.14845}{0.1085}

z = - 1.368

Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.

Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools

You might be interested in
Find two numbers such that the sum of the first and three times the second is 5 and the sum of the second and two times the firs
Sav [38]

Answer:

first number= 19/5

second number= 2/5

Step-by-step explanation:

first number= a

second number= b

a+3b=5   equation 1

b+2a=8  equation 2

using equation 2 we have

b=8-2a

using equation 1 we have

a+3(8-2a)=5  

a+24-6a=5

24-5=6a-a

19=5a

a=19/5 = first number

so using b=8-2a

we have

b=8-2(19/5)

b=8-(38/5)

b=2/5 = second number

4 0
3 years ago
Why did Sasuke have to kill Itachi though :(
sineoko [7]

Answer:

cuz one punch man was coming

5 0
2 years ago
Read 2 more answers
Solve for x. Please show work.
abruzzese [7]

Answer:

x= to 5

Step-by-step explanation:


5 0
2 years ago
Betty's height is 2/3 of Jinlan's height. Find the ratio of Betty's height to Jinlan's height.
nasty-shy [4]
Betty's height versus Jinlan's height is 2:3
3 0
2 years ago
An item is regularly priced at $83. It is on sale for 95% off the regular price.
natita [175]

Answer:

Step-by-step explanation:

Regular price  = $ 83

Discount  = 95% of 83

               = 0.95 * 83

              = $ 78.85

Price after discount = 83 - 78.85

                                = $ 4.15

7 0
3 years ago
Read 2 more answers
Other questions:
  • When given 36 cubes, list 4 ways rectangular prisms can be created with a volume of 36 cubic units
    7·1 answer
  • Please help I haven’t been to school in a while and I need help
    11·2 answers
  • What is the area of a parallelogram if is length is x+4 and height is x+3?
    5·1 answer
  • An aquarium has a length of nº + 2 inches, a height of
    7·1 answer
  • An equation that involves a number raised to a variable power is?....Vocab word
    5·1 answer
  • Your computer supply store sells two types of inkjet printers. The first, type A, costs $267 and you make a $24 profit on each o
    14·1 answer
  • I need help with math can someone help me I’ll show the question?
    14·1 answer
  • PLS help me<br> if you get it right i will give brainliest
    12·1 answer
  • WHat is the largest multiple of 5 that is less than 24
    8·1 answer
  • Expressions in brackets should always be calculated first. If there are no brackets in an algebraic expression, it means that mu
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!