4 of 5 SHORT ANSWER. Write the word or phrase that best completes each statement

Question

4 of 5 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Identify the null hypothesis, alternative hypothesis, test statistic, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use TRADITIONAL method.(10 CREDITS) 16) A poll of 1068 adult Americans reveals that 48% of the voters surveyed prefer the 16) Democratic candidate for the presidency. At the 0.05 level of significance, test the claim that at least half of all voters prefer the Democrat.

Explanation / Answer

Here we have to test the hypothesis that,

H0 : p >= 0.5 Vs H1 : p < 0.5

where p is population proportion for all voters prefer the Democrat.

Assume alpha = level of significance = 0.05

Given that,

sample size (n) = 1068

sample proportion (p^) = 48% = 0.48

Now test statistic is,

Z = (p^ - p) / sqrt(p*q) / n

where q = 1-p = 1 - 0.5 = 0.5

Z = (0.48 - 0.5) / sqrt(0.5*0.5)/1068 = -1.31

Now we have to find P-value for taking decision.

P-value we can find in EXCEL.

syntax :

=NORMSDIST(z)

where z is test statistic

P-value = 0.0956

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that at least half of all voters prefer the Democrat.

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