Represent a three-dimensional figure with a circular base

A pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome). In the first sta

Akimi4 [234]

Answer:

95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

Step-by-step explanation:

We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).

In the first stages of a clinical trial, it was successful for 7 out of the 14 women.

Firstly, the pivotal quantity for 95% confidence interval for the true proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of women who find success with this new treatment = $\frac{7}{14}$ = 0.50

n = sample of women = 14

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the true proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.50-1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ , $0.50+1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ ]

= [0.238 , 0.762]

Therefore, 95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

4 0

4 years ago

Determine the area of an isosceles right triangle with the equal sides each measuring 10 cm in length

Akimi4 [234]

Check the picture below.

6 0

3 years ago

Question 1

Luden [163]

Answer:

>this is your answer this is write

8 0

3 years ago

An isosceles triangle has a perimeter of 36 inches. Its base is 2

astra-53 [7]

The lengths of the sides of the triangle are 8, 8, 20

Explanation:

Given that the perimeter of an isosceles triangle is 36 inches.

The base of the triangle is $2\frac{1}{2}$ times longer than each of its legs.

We need to determine the lengths of the sides of the triangle.

Lengths of the sides:

Let x denote the lengths of the sides of the triangle.

The base of the triangle is given by

$2\frac{1}{2}x=\frac{5}{2}x=2.5x$

Perimeter of the isosceles triangle = Sum of the three sides of the triangle.

Thus, we have,

$36=x+x+2.5x$

$36=4.5x$

$8=x$

Thus, the length of the sides of the isosceles triangle is 8 inches.

Base of the triangle = $2.5(8)=20 \ inches$

Hence, the three sides of the isosceles triangle are 8, 8, 20

3 0

4 years ago

#14 The sum of a number and four is no more than 13

Genrish500 [490]

Answer:

$\Huge \boxed{N$

Step-by-step explanation:

To solve this problem, first you have to isolate it on one side of the equation. Subtraction property of equality is subtract from both sides of an equation the same number doesn't change the equation.

First, subtract 4 from both sides.

$\displaystyle n+4-4$

Solve.

$\displaystyle 13-4=9$

In conclusion, the correct answer is n<9.

3 0

4 years ago

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