Question

a poll of 1012 americans showed that 47.4% of the respondents prefer to watch the news rather than read or listen to it. use those results with a 0.01 significance level to test the claim that fewer than half of americans prefer to watch the news rather than read or listen to it. use the p - value method. use the normal distribution as an approximation to the binomial distribution.

h₀: p = 0.5
h₁: p < 0.5
(type integers or decimals. do not round.)

identify the test statistic.

z = - 1.65
(round to two decimal places as needed.)

identify the p - value.

p - value = □
(round to three decimal places as needed.)

Explanation:

Step1: Find the P - value for the left - tailed test

For a left - tailed z - test, the P - value is \(P(Z\lt z)\), where \(z=-1.65\).
Using the standard normal distribution table or a calculator with a normal distribution function (\(P(Z\lt z)\) function), we find the value corresponding to \(z = - 1.65\).

Step2: Calculate the P - value

Looking up \(z=-1.65\) in the standard normal table:
The area to the left of \(z = - 1.65\) is \(0.0495\) (using a standard normal table or a calculator like \(\text{normalcdf}(-\infty,-1.65)\) on a TI - 84 Plus: \(\text{normalcdf}(-1000,-1.65,0,1)\) where \(-1000\) is used to approximate \(-\infty\), mean \(\mu = 0\) and standard deviation \(\sigma=1\)).

Answer:

\(0.050\) (rounded to three decimal places)