Question

The Civil War. Suppose a national survey conducted among a simple random sample of 1538 American adults, 825 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 =

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

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

Answer 1

Solution-A"

OPTION C

. ?0:?=0.5

??:?>0.5

2. Calculate the test statistic for this hypothesis test.  ? z =

z=p^-/qrt(p*(1-p)./n

p^=825/1538=0.5364109

z=(0.5364109-0.5)/sqrt(0.5*(1-0.5)/1538)

z=2.8559

z=2.8559

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

p=2*(1-Right tail)

Right tail prob in excel

=NORMSDIST(2.8559)

=0.997854

left tail=1-0.997854=0.002145751

so p for two tail=2*0.002145751

=0.004291503

p=0.0043

p=0.0043

4. Based on the p-value, we have:

p<0.05

Reject Ho

Accept Ha

As p value is less than 0.01

here p=0.0043

so strong evidence

C. strong evidence