Mathematics, 06.08.2019 22:20 sulseralanna

Arandom sample of 100 students at a high school was asked whether they would ask their father or mother for with a homework assignment in science. a second sample of 100 different students was asked the same question for an assignment in history. forty-three students in the first sample and 47 students in the second sample replied that they turned to their mother rather than their father for . construct a 98% confidence interval for p 1 - p 2.

Answers: 3

Show answers

Answers

Answer from: bermudezsamanth

98% confidence interval is given as [-0.204, 0.124]

Step-by-step explanation:

In this question we have given

number of student in sample-1, $N_{1}=100$

number of student in sample-2, $N_{2}=100$

43 students in the first sample and 47 students in the second sample replied that they turned to their mother rather than their father for help

Therefore,

$p_{1}=\frac{43}{100}$

$p_{1}=0.43$

and

$p_{2}=\frac{47}{100}$

$p_{2}=0.47$

$p_{1}-p_{2}=0.43-0.47\\p_{1}-p_{2}= -0.04$

and we can determine p by using following formula,

$p = \frac{n_{1}p_{1}+n_{2}p_{2} }{n_{1}+n_{2}}$ ..............(1)

put values of $n_{1},n_{2},p_{1}$ and $p_{2}$ in equation (1)

$p = \frac{100\times .43+100\times .47}{100+100}$

$p = \frac{43+47}{200}$

$p = \frac{90}{200}$

p =.45

Now we can determine q by using following formula

q=1-p ................(2)

put value of p in equation 2

q =1-.45

q =.55

Now we can determine Standard Error of the difference between population proportions by using following formula

Standard error

= $\sqrt{pq(\frac{1}{n_{1}}+\frac{1}{n_{2} })$ .............(3)

Standard error

= $\sqrt{.45\times .55(\frac{1}{100}+\frac{1}{100})$

Standard error

= $\sqrt.2475\times .02$

standard error=0.07035

standard error=0.0704

z- score for 98% confidence is 2.3263

Now we can determine lower limit of confidence interval by using following formula

= $(p1 - p2) - 2.3263\times$ standard error

lower limit of confidence interval = $(.43-0.47) - 2.3263\times0.0704$

lower limit of confidence interval = $-0.04 - 2.3263\times0.0704$ lower limit of confidence interval=-0.2038

Similarly we can determine upper limit of confidence interval by using following formula

= $(p1 - p2) +2.3263\times$ standard error

Therefore,

Upper limit of confidence interval = $(.43-0.47) + 2.3263\times0.0704$

Upper limit of confidence interval = $-0.04 +2.3263\times0.0704$

Upper limit of confidence interval= 0.1238

Therefore,

98% confidence interval is given as [-0.204, 0.124]

Answer from: Quest

ege

step-by-step explanation:

egge

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Another question on Mathematics

Mathematics, 21.06.2019 21:20

Christine wong has asked dave and mike to her move into a new apartment on sunday morning. she has asked them both, in case one of them does not show up. from past experience, christine knows that there is a 40% chance that dave will not show up and a 30% chance that mik a. what is the probability that both dave and mike will show up? (round your answer to 2 decimal places.) b. what is the probability that at least one of them will show up? c. what is the probability that neither dave nor mike will show up? (round your answer to 2 decimal places.)e will not show up. dave and mike do not know each other and their decisions can be assumed to be independent.

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

For the feasibility region shown below find the maximum value of the function p=3x+2y

Answers: 3

Answer

Mathematics, 22.06.2019 00:30

Asalsa recipe uses green pepper, onion, and tomato in the extended ratio 3: 5: 7. how many cups of tomato are needed to make 105 cups of salsa? a. 7 b. 21 c. 35 d. 49

Answers: 3

Answer

Mathematics, 22.06.2019 02:00

Your company will replace the asphalt roofs on all the buildings at the factory complex shown below. the buildings have flat roofs. you charge according to the total roof area. what is this area, in square yards?

Answers: 3

Answer

You know the right answer?

Arandom sample of 100 students at a high school was asked whether they would ask their father or mot...

Questions