MATHEMATICS COLLEGE

Suppose you wanted to estimate the difference between two population means correct to within 4.8 at the 92% confidence level. If prior information suggests that both population variances are approximately equal to 12 and you want to select independent random samples of equal size from the populations, how large should the sample sizes be?Critical Value: 1.75
The sample sizes should be: n1=_n2=___?

Answers

Answer 1

Answer:

Answer: $n_1=n_2=4$

Step-by-step explanation:

Given : Margin of error : E= 4.8

Confidence level : 92%

Significance level : $1-0.92=0.08$

$\sigma_1^2=\sigma_1^2\approx12$

Two-tailed critical value :-

$z_(\alpha/2)=z_(0.08/2)=z_(0.04)=1.75$

If we want to select independent random samples of equal size from the populations,

Formula for the sample size :

$n_1=n_2=((z_(\alpha/2))/(E))^2(\sigma_1^2+\sigma_2^2)$

Then buy using given values , we have

$n_1=n_2=((1.75)/(4.8))^2(12+12)$

Simplify ,

$n_1=n_2=((1.75)/(4.8))^2(12+12)=3.190\approx4$ [Round to the next integer.]

Hence, the The sample sizes should be: $n_1=n_2=4$

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The probability that a boy is born with Down's syndrome is p, 0

Answers

Answer:

The probability that a baby born with Down's syndrome is a boy is $(p)/(p+q)$ .

Step-by-step explanation:

The probability of a baby born being a boy (B) or a girl (G) is same, i.e.

P (B) = P (G) = 0.50.

The probability of a boy is born with Down's syndrome is, P (D|B) = p.

The probability of a girl is born with Down's syndrome is, P (D|G) = q.

The law of total probability states that:

$P(X)=P(X|Y)P(Y)+P(X|Z)P(Z)$

Use this law to compute the probability of a baby born with Down's syndrome as follows:

$P(D)=P(D|B)P(B)+P(D|G)P(G)\n=(p*0.50)+(q*0.50)\n=0.50(p+q)$

The conditional probability of an event X given that another event Y has already occurred is:

$P(X|Y)=(P(Y|X)P(X))/(P(Y))$

Compute the probability that a baby born with Down's syndrome is a boy as follows:

$P(B|D)=(P(D|B)P(B))/(P(D)) =(p*0.50)/(0.50(p+q)) =(p)/(p+q)$

Thus, the probability that a baby born with Down's syndrome is a boy is $(p)/(p+q)$ .

Complete the following statement. 3(4 x 8) (3 x4) (_)

Answers

Answer:

Step-by-step explanation:

(8*4)3=96

3*4=12

12*8=96

Find the value of x.

x=

Answers

Answer:

my guess is 135 because there both the same corners

Step-by-step explanation:

Answer:

110

Step-by-step explanation:

900-(105+150+140+135+125+135)= 110

Michael started a savings account with $300. After 4 weeks, he had $350 dollars, after 9 weeks, he had $400. What is the rate of change of money in his savings account per week?

Answers

Answer:

$12.50 per week

Step-by-step explanation:

See photos

Read first four weeks first

then read next four weeks

last read over eight weeks

Jeremy sprinted for 123 seconds and rested. Then he sprinted for 157 seconds, rested, and sprinted again for 195 seconds. Estimate the combined time he sprinted by rounding to the nearest ten and then adding the rounded numbers.

Answers

480 aproxmately if you round the numbers then add them up

The floor of a shed given on the right has an area of 44 square feet . The floor is in the shape of a rectangle whose length is 3 less than twice the width. Find the length and width of the floor of the shed.

Answers

Answer:

The length and width of the floor of the shed are 8 feet and 5.5 feet, respectively.

Step-by-step explanation:

Given that the shape of the shed is a rectangle, the expression for the area is:

$A = w \cdot l$

Where $w$ and $l$ are the width and length of the shed, measured in feet. In addition, the statement shows that $l = 2\cdot w - 3\,ft$ . Then, the equation of area is expanded by replacing length: