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]
2 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]2 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
Ellie has a bank account balance of -$43.39 if she makes it deposited $50 in your account what will be her new balance?
Nadusha1986 [10]

Her new balance should be $6.61.  

6 0
3 years ago
Read 2 more answers
Luna mixes 3/4 cup of orange juice with 3/8 cup of cranberry juice. She gives 5/8 cup of juice to mags. How much is left in luna
Anuta_ua [19.1K]

Answer:

\frac{1}{2}  \: cup \: of \: juice

Step-by-step explanation:

See the attached picture for explanation.

5 0
3 years ago
What is the greatest possible product of a 2-digit number and a 1-digit number.Explain how you know
Elodia [21]
The answer is 891. 99 is the greatest 2 digit number and 9 is the greatest 1 digit number. So the product of the two (multiply them) gives you your answer of 891 (99 x 9 = 891).
7 0
2 years ago
In circle O, the length of radius OL is 6 cm and the length of arc LM is 6.3 cm. The measure of angle MON is 75°
djyliett [7]

Answer:

14.2cm

Step-by-step explanation:

Complete question:

<em>In circle O, the length of radius OL is 6 cm and the length of arc LM is 6.3 cm. The measure of angle MON is 75°.  </em>

<em>Rounded to the nearest tenth of a centimeter, what is the length of arc LMN?  </em>

<em></em>

Find the diagram attached

arc LN= arc  LM + arc MN

First we need to get the arc MN

length of an arc = theta/360 * 2πr

length of arc MN = 75/360 * 2(3.14)(6)

length of arc MN = 0.20833*37.68

length of arc MN = 7.85

Hence;

arc LN = 6.3 + 7.85

arc LN = 14.15cm

Hence the length of arc LN is 14.2cm

8 0
3 years ago
9p + 8 Math fraction
Klio2033 [76]

Answer:

17p

Step-by-step explanation:

9p+8p=17p

8 0
3 years ago
Other questions:
  • Okay random but if you think Michael Jackson and Bruno Mars are good singers and dancers. Plz respond just curious???
    5·2 answers
  • 99 Points!!!
    10·2 answers
  • Write an equation that shows the equivalency between meters and gigameters.
    13·1 answer
  • PLZ CHECK MY ANSWER. Round your answer to the nearest tenth.
    15·1 answer
  • Solve 4x - c=k for x
    9·2 answers
  • 7 out of 10 doctors prefer cough syrup over any competitors. Using the given ratio, answer the following questions. out of 500 t
    8·1 answer
  • 4. Assume that you have a part-time job at which you work 20 hours per week at the rate
    5·1 answer
  • Consider the function , f(x)=4x-5 what is the domain value that correspond to an output of f(x) = 11
    13·1 answer
  • Translate the phrase into an algebraic expression: 12acorns per qsquirrels?
    13·1 answer
  • 14 Type the correct answer in each box. Use numerals instead of words. a Ava, Lucas, and Maria are playing a game where they pas
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!