Question

The Civil War. Suppose a national survey conducted among a simple random sample of 1549 American adults, 802 indicate that they think the Civil War is still relevant to American politics and political life.

NOTE: While performing the calculations, do not used rounded values. For instance, when calculating a p-value from a test statistic, do not use a rounded value of the test statistic to calculate the p-value. Preserve all the decimal places at each step.

Enter at least 4 decimal places for each answer in WeBWorK.

1. What are the correct hypotheses for conducting a hypothesis test to determine if the majority (more than 50%) of Americans think the Civil War is still relevant.

A. ?0:?=0.5H0:p=0.5, ??:?>0.5HA:p>0.5
B. ?0:?=0.5H0:p=0.5, ??:?<0.5HA:p<0.5
C. ?0:?=0.5H0:p=0.5, ??:?≠0.5HA:p≠0.5

2. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

3. Calculate the p-value for this hypothesis test.

4. Based on the p-value, we have:
A. some evidence
B. extremely strong evidence
C. little evidence
D. strong evidence
E. very strong evidence
that the null model is not a good fit for our observed data.

Answer 1

1)

Ho :   p =    0.5
H1 :   p >   0.5

2) z test

3)

Number of Items of Interest,   x =   802                  
Sample Size,   n =    1549                  
                          
Sample Proportion ,    p̂ = x/n =    0.5178                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0127                  
Z Test Statistic = ( p̂-p)/SE = (   0.5178   -   0.5   ) /   0.0127   =   1.3975
                          
  
p-Value   =   0.0811   [Excel function =NORMSDIST(-z)              

4) C. little evidence