Question

Problem 1: Use the following to answer questions a) – e): In a survey conducted by the Gallup organization September 6-9, 2012, there were 1,017 adults asked "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" Of the 1,017 respondents, 214 said they had "no confidence at all." The research question: Does this sample provide evidence that the proportion of U.S. adults who have no confidence in the media differs significantly from 25%. a. State the hypotheses for testing if this data provides evidence that the proportion of U.S. adults who have no confidence in the media differs significantly from 25%. Use proper notation. (3 points) b. Verify that it is appropriate to use a normal distribution to compute the p-value. Please show your work. (Hint: The conditions are indicated on the provided formula sheet!) (2 points) C. Use the provided formula sheet to identify the appropriate test statistic formula. Then calculate the test statistic. Please show all of your work including the formula that you are using. (4 points)
please help

Answer 1

a)

Ho :   p =    0.25  
H1 :   p ╪   0.25   (Two tail test)

b)

sample size,n < 5% of population size,N  
np>5 and n(1-p)>5 = 6.3

c)

Level of Significance,   α =    0.05   
Number of Items of Interest,   x =   214  
Sample Size,   n =    1017  
          
Sample Proportion ,    p̂ = x/n =    0.2104  
          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0136  
Z Test Statistic = ( p̂-p)/SE =    (0.2104-0.25)/0.0136=   -2.91  
          
d)
          
p-Value   =   0.0036   [excel formula =2*NORMSDIST(z)]

e)

Decision:   p-value<α , reject null hypothesis       
There is enough evidence that proportion differs significantly from 25%

Please let me know in case of any doubt.

Thanks in advance!

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