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
Korolek [52]
3 years ago
11

It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first epi

sode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 163 people in the first group and this group will be administered the new drug. There are 160 people in the second group and this group wil be administered a placebo. After one year, 13% of the first group has a second episode and 14% of the second group has a second episode. Select a 90% confidence interval for the difference in true proportion of the two groups.
a) [0.00590, 0.0251].
b) [0.00690, 0.0551].
c) [0.0890, 0.0551].
d) [0.00690, 0.0351].
e) [0.00890, 0.0651].
Mathematics
1 answer:
ElenaW [278]3 years ago
5 0

Answer:

90% confidence interval for the difference in true proportion of the two groups is (-0.0717, 0.0517).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

First group: Sample of 163, 13% has a second episode.

This means that:

p_1 = 0.13, s_1 = \sqrt{\frac{0.13*0.87}{163}} = 0.026

Second group: Sample of 160, 14% has a second episode

This means that:

p_2 = 0.14, s_2 = \sqrt{\frac{0.14*0.86}{160}} = 0.027

Distribution of the difference:

p = p_1 - p_2 = 0.13 - 0.14 = -0.01

s = \sqrt{s_1^2+s_2^2} = \sqrt{0.026^2+0.027^2} = 0.0375

Confidence interval:

The confidence interval is:

p \pm zs

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

90% confidence level

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

Lower bound:

p - 1.645s = -0.01 - 1.645*0.0375 = -0.0717

Upper bound:

p + 1.645s = -0.01 + 1.645*0.0375 = 0.0517

90% confidence interval for the difference in true proportion of the two groups is (-0.0717, 0.0517).

You might be interested in
If the volume of sand is increasing at a constant rate, is the height increasing at a constant rate? Explain.
AysviL [449]
It does not necessarily mean that the height will rise although I it could rise.this is because volume is what is inside your shape. It could spread out more and have more volume. If you think I'm smart let me tell you I'm only in 4th grade not bragging
4 0
3 years ago
Solve. If this is no solution write s { }<br> 5x-9&gt;8+5x
german
The answer is there are no solution
3 0
2 years ago
Find the equation that is perpendicular to 7y= -3x passing through (9,1).
Lera25 [3.4K]

Answer:y=7/3x−20. that is the equation that is perpendicular.

8 0
3 years ago
Can you answer this? <br> factorise 6p + 24q
Talja [164]

Answer:

6(p+4q)

Step-by-step explanation:

6 0
3 years ago
find the present value of an investment that is worth $19,513.75 after earning 3percent simple interest for 5.5 years
Dahasolnce [82]

Answer:

present value = $16750

Step-by-step explanation:

The simple interest formula allows us to calculate A, which is the final amount. According to this formula, the amount is given by A = P (1 + r*t), where P is the principal, r is the annual interest rate in decimal form, and t is the loan period expressed in years

simple interest formula:

t: time

P: present value

A: amount

r : anual interest

A = P (1 + r*t)

P = A / (1 + r*t)

P = 19,513.75 / (1 + 3/100 * 5.5)

P = 19,513.75/ (1 + 0.165)

P = 19,513.75 / 1.165

P = 16750

present value = $16750

5 0
3 years ago
Other questions:
  • For any distribution, what is the z-score corresponding to the median? 0 1 n cannot be determined from the information given
    5·1 answer
  • Jeremy says that 5.676677666777... is a rational number because it is decimal that goes on forever
    13·1 answer
  • I need help please help me
    10·1 answer
  • Could some help me please I’m stuck on this
    8·1 answer
  • Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes.
    15·1 answer
  • 84,600,600 Write each number in scientific notation
    9·1 answer
  • 6<br> 4.<br> 2<br> 74-22<br> 2<br> 4-<br> 6<br> Slope
    9·1 answer
  • A regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: ŷ = 50,000 − 8x The a
    15·1 answer
  • 1.935 people visit a library during one week.
    11·1 answer
  • PLEASE HELP!!! i can’t find the answer
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!