After President Obama\'s re-election, a mass shooting in Newtown. Connecticut, p

Question

After President Obama's re-election, a mass shooting in Newtown. Connecticut, prompted him to propose new laws intended to reduce gun violence. Politicians are more likely to vote for a law when a majority, or more than half, of voters support it. To test the claim (at a 5% significance level) that a majority of adults in the U.S. supported Obama's proposals, Gallup randomly sampled 1, 021 adults in the U.S. and found that 541 supported the president. You determined the null and alternative hypotheses in Question 1C in the lesson. Give them again below. H_0: __________ H_0: __________Is this a right-tailed, left-tailed, or two-tailed test? You have made an assumption about the population proportion (p) above. Now we need the sample size (n) and sample proportion (p). n = ____________ p^cap = ___________Are the criteria for approximate normality satisfied?

Explanation / Answer

Part A

The null and alternative hypotheses are given as below:

Null hypothesis: H0: No more than half of the voters support the new law.

Alternative hypothesis: More than half of the voters support the new law.

H0: p 0.5

Ha: p > 0.5

Part B

This is a right tailed test because, alternative hypothesis consist of ‘>’ type.

Part C

n = 1021

x = 541

p = x/n = 541/1021 = 0.529873

Part D

We are given, n = 1021 and p = 0.50, q = 1 – p = 1 – 0.5 = 0.5

For normal approximation, we have to check whether n*p > 5 and n*q > 5

So, n*p = 1021*0.50 = 510.5 > 5 and n*q = 1021*0.5 = 510.5 > 5

So, criteria for normal approximation are satisfied.

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