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
matrenka [14]
3 years ago
15

A magazine reports that women trust recommendations from a particular social networking site more than recommendations from any

other social network platform. But does trust in this social networking site differ by gender? The following sample data show the number of women and men who stated in a recent sample that they trust recommendations made on this particular social networking site.
Women Men
Sample 150 170
Trust Recommendations Made-
on the social networking site 123 102

(a) What is the point estimate of the proportion of women who trust recommendations made on this particular social networking site?
(b) What is the point estimate of the proportion of men who trust recommendations made on this particular social networking site?
(c) Provide a 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on this particular social networking site. (Round your answers to four decimal places.)
Mathematics
1 answer:
Scilla [17]3 years ago
8 0

Answer:

(0.82-0.6) - 1.96\sqrt{\frac{0.82(1-0.82)}{150} +\frac{0.6(1-0.6)}{170}}=0.1241  

(0.82-0.6) + 1.96\sqrt{\frac{0.82(1-0.82)}{150} +\frac{0.6(1-0.6)}{170}}=0.3159  

And the 95% confidence interval would be given (0.1241;0.3159).  

We are confident at 95% that the difference between the two proportions is between 0.1241 \leq p_A -p_B \leq 0.3159

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Part b

p_A represent the real population proportion for male

\hat p_A =\frac{123}{150}=0.82 represent the estimated proportion for male

n_A=150 is the sample size required for male

Part a

p_B represent the real population proportion for female

\hat p_B =\frac{102}{170}=0.6 represent the estimated proportion for male

n_B=170 is the sample size required for female

z represent the critical value for the margin of error  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})  

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}  

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.96  

And replacing into the confidence interval formula we got:  

(0.82-0.6) - 1.96\sqrt{\frac{0.82(1-0.82)}{150} +\frac{0.6(1-0.6)}{170}}=0.1241  

(0.82-0.6) + 1.96\sqrt{\frac{0.82(1-0.82)}{150} +\frac{0.6(1-0.6)}{170}}=0.3159  

And the 95% confidence interval would be given (0.1241;0.3159).  

We are confident at 95% that the difference between the two proportions is between 0.1241 \leq p_A -p_B \leq 0.3159

You might be interested in
Which comparison is not correct?
strojnjashka [21]

Answer:

the 2 one is wrong

Step-by-step explanation:

the 2 would be greater than the 9 sense both the numbers are negative and the bigger the negative number is the less amount it is so -9 is smaller than -2

8 0
2 years ago
What is [48(72-12) -15x15]÷9
Angelina_Jolie [31]

Answer:

295

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
I don’t get this can someone please help me
s344n2d4d5 [400]

Answer:

A, B,

Step-by-step explanation:

7 0
3 years ago
The 7th term of an arithmetic sequence is 1, and the 20th term is -25. find the 25th term.
Natasha_Volkova [10]
A(7)=1
a(20)=25
a(25)=?

a(n)=a(1)+d(n-1)

a(7)=a(1) +6d=1         -11/13+6*24/13= 
a(20)=a(1)+19d=-25

a(1) +6d=1
a(1)+19d=-25 (subtract first equation from the second)
---------------------
      19d-6d =-26
       13d =-26
d=-2

a(1)=1-6d=1-6*(-2)=13

a(25)= a(1)+d(25-1)= 13+(-2) *24= 13-48=-35
7 0
3 years ago
In what way do bushes benefit from bears. eating their berries
tiny-mole [99]

Answer:

They have spikes???

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • PLEASE HELP ASAP!! BRAINLIEST FOR BEST ANSWER
    15·2 answers
  • HELP ME PLEASE I NEED ITTTTTT I WILL REWARD
    12·1 answer
  • Help me I WILL GIVE BRAINLEST
    13·1 answer
  • Michael invested 5,000 in an account that has a 5.5% annual interest rate. What equation best describes investment after T years
    13·1 answer
  • If u = 4 inches, v = 5, w = 7 inches, x = 6 inches, y = 8 inches, and z = 5 inches, what is the area of the object
    11·1 answer
  • Plzzxzzzzzzzzzzzzzzzzzxxzbxbxbxbx lol
    8·2 answers
  • HELP PLEASE BE QUICK WILL GIVE BRAINLIEST.
    10·1 answer
  • A hot air balloon is dropping from a height above the ground at a steady rate of 8 feet per second. It starts from a height of 7
    8·1 answer
  • Seven days ago, the gas tank on Rosa's car was filled with 20 gallons of gasoline. Today there are 6 gallons of gasoline. a. Wha
    14·1 answer
  • The equation for the circle below is x2 + y2 = 16. What is the length of the<br> circle's radius?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!