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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

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otez555 [7]

Answer:

John is 9.21 km form the school.

Step-by-step explanation:

John leaves school to go home. His bus drives 6 kilometres north and then goes 7 kilometres west. It is required to find John's distance from the school. It is equal to the shortest path covered or its displacement. So,

d=\sqrt{6^2+7^2} \\\\d=9.21\ km

So, John is 9.21 km form the school.

5 0
3 years ago
Show that there is no solution for the radical equation 4w+4=-4.
Ad libitum [116K]

Answer:

there is a solution

w= -2

Step-by-step explanation:

4w+4=-4

    -4    -4

4w=-8

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3 0
3 years ago
The table shows the American League batting champions for the years 1999–2003. The sum of these five batting averages is 1.754.
fgiga [73]
The answer is <span>A. .357 + .372 + .350 + .349 + x = 1.754; .326 
</span>
x1 - average of <span>1999 Nomar Garciaparra Boston
</span>x2 - average of 2000 Nomar Garciaparra Boston
x3 - average of <span>2001 Ichiro Suzuki Seattle 
</span>x4 - average of Manny Ramirez Boston  
x - average of <span>2003 Bill Mueller Boston 

</span><span>The sum of these five batting averages is 1.754:
x1 + x2 + x3 + x4 + x = 1.754

From the table:
x1 = 0.357
x2 = 0.372
x3 = 0.350
x4 = 0.349
x = ?

<u>0.357 + 0.372 + 0.350 + 0.349 + x = 1.754</u>

1.428 + x = 1.754
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5 0
3 years ago
Can someone help me with this guys? Thank you so much! I mark as brainliest
Vitek1552 [10]

Answer:

y=45

x=9

z= 9 root 2

Step-by-step explanation:

This is a right isosceles triangle, so

y=45

x=9

z= 9 root 2

9²+9²=z²

81+81=z²

162=z²

√162=z

z=9√2

5 0
3 years ago
Youre purchasing a new television with a 32" screen. the 32" measurement represents the diagonal measurement of the screen. You
Nonamiya [84]

Answer:

B. 28 inches

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem.

a^2 +b^2 =c^2  where a and b are the legs and c is the hypotenuse (diagonal)

16^2 + b^2 = 32^2

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Subtract 256 from each side

256-256 + b^2 =1024-256

b^2 = 768

Take the square root of each side

sqrt(b^2) = sqrt(768)

b = 27.7128129

Rounding to the nearest inche

b = 28 inches

3 0
3 years ago
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