Question

In November 2009, 65% of Americans favored the death penalty for a person convicted of murder. In November 2014, 1250 adult Americans were asked by the Gallup organization, “Are you in favor of the death penalty for a person convicted of murder?” Of those surveyed, 783 responded yes. Use this survey data to test whether the proportion of Americans who favored the death penalty for a person convicted of murder had changed from 2009 to 2014 at level of significance α = 0.10.

Conditions:
np₀(1-p₀) =  (Round to 3 decimal places.)
The normal approximation test for proportions  (is / is not) appropriate for this data.

Rejection Region:
To test the given hypotheses, we will use a (left / right / two) -tailed test.  
The appropriate critical value(s) for this test is/are .  (Report your answer exactly as it appears in Table V. For two-tailed tests, report both critical values in the answer blank separated by only a single space.)

On a separate sheet of paper, sketch the rejection region(s) for this test. You will need this sketch in Question 4.

The sample proportion is p^ = . (Round to 3 decimal places.)
The test statistic for this test is z₀=.  (Calculate this value in a single step in your calculator using the rounded sample proportion reported above, and report your answer rounded to 3 decimal places.)

Label the test statistic in your sketch from Question 3. Use this sketch to conclude the hypothesis test.

We  (reject / fail to reject) H₀.
The given data  (does / does not) provide significant evidence that the proportion of Americans who favored the death penalty for a person convicted of murder had changed from 2009 to 2014.

Answer 1

Ans:

np₀(1-p₀) =1250*0.65*(1-0.65)=284.375

The normal approximation test for proportions is appropriate for this data.

two-tailed test  

Critical values are -1.645 and 1.645

blue shaded region are critical rejection regions.

4)

sample proportion=783/1250=0.626

Test statistic:

z=(0.626-0.65)/sqrt(0.65*(1-0.65)/1250)

z=-1.779

As,test statistic falls in the rejection region,We  reject H₀.

The given data  does provide significant evidence that the proportion of Americans who favored the death penalty for a person convicted of murder had changed from 2009 to 2014.