Is there public support in a large regional city for the introduction of an annu

Question

Is there public support in a large regional city for the introduction of an annual music festival to boost tourism? In a reputable poll of 800 randomly chosen adults in the city, 45% indicated that they supported the concept of an annual music festival, whereas 43% indicated the reverse. (a) Find a 98% confidence interval for p, the overall proportion of adults in the city who support the concept of an annual music festival. (b) Do you think that the majority of adults in this city support the concept of an annual music festival? Justify your answer.

Explanation / Answer

Question a)

P^ = 0.45

n = 800

Confidence Level = 98%

Formula for Confidence Interval:

P^ ( - / +) E

E = zc * sqrt ( (p^ * (1-p^))/n)

zc is the critical value for 2% level of significance from normal table we get it as 2.33

E = 2.33 * sqrt ((0.45*(1-0.45))/800) = 0.0410

P^ (-/+) E

0.45 (-/+)0.0410

0.409 and 00.491

Answer: The 98% confidence interval is 0.409 and 0.491

Question b)

Answer: The confidence interval does not contain the proportion of 50% ( or > ). I do not think that the majority of adults in this city support the concept of an annual music festival.

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