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
Vsevolod [243]
3 years ago
5

Researchers are interested in determining whether more men than women prefer Coca Cola to Pepsi. In a random sample of 300 men,

65% prefer Coca Cola, whereas in a random sample of 400 women, 48% prefer Coca Cola. What is the 99% confidence interval estimate for the difference between the percentages of men and women who prefer Coca Cola over Pepsi? 0.17 ± 0.036 0.17 ± 0.096 0.17 ± 0.067 0.565 ± 0.067 0.565 ± 0.096
Mathematics
2 answers:
kobusy [5.1K]3 years ago
6 0

Answer: 0.17 ± 0.096

Step-by-step explanation:

Confidence interval for difference between the population proportion :

p_1-p_2\pm z^*\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}

, where p_1 = sample proportion for population 1.

 p_2 = sample proportion for population 2.

n_1 = Sample size from population 1.

n_2 = Sample size from population 1.

As per given , we have

Population

p_1=0.65\ \ \& \ \ p_2=0.48

n_1=300\ \ \ \&\ \ n_2=400

Critical z-value for 99% confidence level is z*=2.576  [By z-table]

Now , the 99% confidence interval estimate for the difference between the percentages of men and women who prefer Coca Cola over Pepsi :

(0.65-0.48)\pm (2.576)\sqrt{\dfrac{(0.65)(1-0.65)}{300}+\dfrac{(0.48)(1-0.48)}{400}}\\\\= 0.17\pm(2.576)\sqrt{0.0007583+0.000624}\\\\=0.17\pm(2.576)\sqrt{0.0013823}\\\\=0.17\pm(2.576)(0.03718)\\\\=0.17\pm0.09577568\\\\\approx0.17\pm0.096\

Hence, the correct answer is 0.17 ± 0.096.

Mekhanik [1.2K]3 years ago
6 0

Answer:

0.17 \pm 0.096

Step-by-step explanation:

We are given that Researchers are interested in determining whether more men than women prefer Coca Cola to Pepsi.

For this, In a random sample of 300 men, 65% prefer Coca Cola, whereas in a random sample of 400 women, 48% prefer Coca Cola.

The pivotal quantity for confidence interval is given by;

              P.Q. = \frac{(\hat p_1 - \hat p_2)-(p_1 - p_2)}{\sqrt{\frac{\hat p_1(1- \hat p_1)}{n_1} + \frac{\hat p_2(1- \hat p_2)}{n_2} } } ~ N(0,1)

where,   \hat p_1 = 0.65        \hat p_2 = 0.48

              n_1 = 300         n_2 = 400

So, 99% confidence interval for the difference between the percentages of men and women who prefer Coca Cola over Pepsi is given by;

 P(-2.5758 < N(0,1) < 2.5758) = 0.99 {At 1% significance level, the z table

                                                              gives value of 2.5758}

P(-2.5758 < \frac{(\hat p_1 - \hat p_2)-(p_1 - p_2)}{\sqrt{\frac{\hat p_1(1- \hat p_1)}{n_1} + \frac{\hat p_2(1- \hat p_2)}{n_2} } } < 2.5758) = 0.99

P(-2.5758 * \sqrt{\frac{\hat p_1(1- \hat p_1)}{n_1} + \frac{\hat p_2(1- \hat p_2)}{n_2} }< (\hat p_1 - \hat p_2)-(p_1 - p_2) < 2.5758 * \sqrt{\frac{\hat p_1(1- \hat p_1)}{n_1} + \frac{\hat p_2(1- \hat p_2)}{n_2} } ) = 0.99

P((\hat p_1 - \hat p_2) - 2.5758 * \sqrt{\frac{\hat p_1(1- \hat p_1)}{n_1} + \frac{\hat p_2(1- \hat p_2)}{n_2} } < (p_1 - p_2) < (\hat p_1 - \hat p_2) + 2.5758 * \sqrt{\frac{\hat p_1(1- \hat p_1)}{n_1} + \frac{\hat p_2(1- \hat p_2)}{n_2} } ) = 0.99

So, 99% confidence interval for (p_1 - p_2) =

[ (\hat p_1 - \hat p_2) - 2.5758 * \sqrt{\frac{\hat p_1(1- \hat p_1)}{n_1} + \frac{\hat p_2(1- \hat p_2)}{n_2} } , (\hat p_1 - \hat p_2) + 2.5758 * \sqrt{\frac{\hat p_1(1- \hat p_1)}{n_1} + \frac{\hat p_2(1- \hat p_2)}{n_2} } ]

= [ (0.65 - 0.48) - 2.5758 * \sqrt{\frac{0.65(1- 0.65)}{300} + \frac{0.48(1- 0.48)}{400} } ,  (0.65 - 0.48) + 2.5758 * \sqrt{\frac{0.65(1- 0.65)}{300} + \frac{0.48(1- 0.48)}{400} } ]

= [ 0.17 - 2.5758 * \sqrt{\frac{0.65(1- 0.65)}{300} + \frac{0.48(1- 0.48)}{400} } , 0.17 + 2.5758 * \sqrt{\frac{0.65(1- 0.65)}{300} + \frac{0.48(1- 0.48)}{400} } ]

= [ 0.17 - 0.096 , 0.17 + 0.096 ] = [0.17 \pm 0.096]

Therefore, 99% confidence interval for the difference between the percentages of men and women who prefer Coca Cola over Pepsi is 0.17 ± 0.096 .

     

You might be interested in
Nicholas used a $10 bill to pay for a granola bar that only costs ppp dollars.
Kipish [7]

Answer:

$(10 - p) is the required expression.

Step-by-step explanation:

7 0
2 years ago
Beth is taking out a loan to purchase a new home. She is financing $50,000 for 25 years at an interest rate of 14.25%. What is h
kozerog [31]
The present value (PV) of a loan for n years at r% compounded t times a year where there is equal P periodic payments is given by:

PV=P\left( \frac{1-\left(1+ \frac{r}{t} \left)^{-nt}}{ \frac{r}{t} } \right)

Given that <span>Beth is taking out a loan of PV = $50,000 to purchase a new home for n = 25 years at an interest rate of r = 14.25%. Since she is making the payment monthly, t = 12.

Her monthly payment is given by:

50,000=P\left( \frac{1-\left(1+ \frac{0.1425}{12} \right)^{-25\times12}}{ \frac{0.1425}{12} } \right) \\  \\ =P\left( \frac{1-(1+0.011875)^{-300}}{ 0.011875 } \right)=P\left( \frac{1-(1.011875)^{-300}}{ 0.011875 } \right) \\  \\ =P\left( \frac{1-0.028969}{ 0.011875 } \right)=P\left( \frac{0.971031}{ 0.011875 } \right)=81.770994P \\  \\  \therefore P= \frac{50,000}{81.770994} =\$611.46

Therefore, her monthly payment is about $611.50
</span>
3 0
3 years ago
Help plsssssssssssss????
nikklg [1K]

Answer:

y=2/3+11

Step-by-step explanation:

5 0
3 years ago
Help me answer 2/9 divided by 1/6
Zigmanuir [339]

1.33333

Step-by-step explanation:

Don't worry it checks out.

3 0
3 years ago
Read 2 more answers
Is the following statement always, sometimes, or never true? “The supplement of an acute angle is an obtuse angle.” Explain your
balu736 [363]

Answer:

Always

Step-by-step explanation:

An acute angle is an angle that is less than 90. Supplementary angles add up to 180.

So 180-89= 91

An obtuse angle is any angle that is greater than 90.

Here's a link to a better explanation.

brainly.com/question/14180317

7 0
2 years ago
Read 2 more answers
Other questions:
  • Can you help me find the answer to <br> 3(-6+6x)=18
    9·2 answers
  • I need help to figure out x.
    7·2 answers
  • A radio station spends 1/4 of each 24 hours on public service announcements. How much time is spend on public service announceme
    5·1 answer
  • What is the value of the expression when f = -4, g =5, and h =3/4
    11·1 answer
  • The graph shows the distance, in miles, that Anders traveled over a period of nine hours. Use the graph to determine the constan
    14·1 answer
  • Please help the image is attached
    5·1 answer
  • Solve the<br> 9x+42=4x-13<br> The solution is x=
    5·2 answers
  • B The lines are translations of each other
    9·1 answer
  • Shari buys a box of 60 candles for £125.
    6·1 answer
  • What is the following simplified product? Assume x 0.<br> (sqrt6x^2+4sqrt8x^3)(sqrt9x-xsqrt5x^5)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!