Question

46% of all Americans said protecting the right to own guns is more important. The Pew Research Center surveyed 1267 randomly selected Americans with at least a bachelor’s degree and found that 559 believed that protecting the right to own guns is more important Does this result suggest the proportion of Americans with at least a bachelor’s degree feel greater than the general American population when it comes to gun control? Use the α = 0.1 level of significance.

a)Identify the null and alternative hypotheses

b)Find the test statistics

c)Find the p-value and critical value

d)Decision about null hypotheses

e)Conclusion

Answer 1

Sample size , n=1267

Sample proportion of Americans with at least a bachelor’s degree who said protecting the right to own guns is more important , = 559/1267 = 0.4412

a) Null hypothesis , H0 : p = 0.46

Alternate hypothesis: Ha : p > 0.46

b) Test statistics, z= = = -1.34

c) P- Value = P( Z > -1.34 ) = P( Z < 1.34 ) = 0.90988

   Critical Value , Z(0.1/2) = 1.6449

d)   Since P- VAalue > significance level we fail to reject the null hypothesis

OR

   Since the test statistic is less than the critical value, that means that the test statistic does not lie in the critical region , hence we fail to reject the null hypothesis.

e) Thus there is not enough evidence at 0.1 significance level to support the claim that  the proportion of Americans with at least a bachelor’s degree feel greater than the general American population when it comes to gun control.