Question

An exit poll of 1000 randomly selected voters found that 515 favored measure A. a. Construct a 99% confidence interval for the support of measure A. b. Suppose measure A needs at least 50% support to pass, what are the null and alternative hypotheses if we were to test to see if measure A will pass? c. Compute the p-value of the above test.

Answer 1

Answer:

Step-by-step explanation:

Given that an  exit poll of 1000 randomly selected voters found that 515 favored measure A.

Sample proportion p = $\frac{515}{1000} =0.515$

$q=1-0.515 =0.485\\n =1000\\SE = \sqrt{\frac{pq}{n} } \\=0.158$

Margin of error 99% = 2.58*SE

=$2.58*0.0158\\=0.0408$

99% confidence interval =$(0.515-0.0408, 0.515+0.0408)\\= (0.474, 0.556)$

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$H_0: p =0.5\\H_a: p >0.5$

(Right tailed test)

STd error = $\sqrt{\frac{0.5*0.5}{1000} } \\=0.0158$

Test statistic Z = p diff/std error =$\frac{0.015}{0.0158} \\\\=0.9487$

p value = 0.1714