in a random sample of 150 voters, 60 support Trump. Set up a 96 percent confidence interval for the proportion of voters who sup
1 answer:
Given:
n = 150, sample size
Denote the sample proportion by q (normally written as
).
That is,
q = 60/150 = 0.4, sample proportion.
At the 96% confidence level, the z* multiplier is about 2.082, and the confidence interval for the population proportion is
![q \pm z^{*}[ \frac{q(1-q)}{ \sqrt{n} } ]](https://tex.z-dn.net/?f=q%20%5Cpm%20z%5E%7B%2A%7D%5B%20%5Cfrac%7Bq%281-q%29%7D%7B%20%5Csqrt%7Bn%7D%20%7D%20%5D)
That is,
0.4 +/- 2.082* √[(0.4*0.6)/150]
= 0.4 +/- 0.0833
= (0.3167, 0.4833)
= (31.7%, 48.3%)
Answer: The 96% confidence interval is about (32% to 48%)
n = 150, sample size
Denote the sample proportion by q (normally written as
That is,
q = 60/150 = 0.4, sample proportion.
At the 96% confidence level, the z* multiplier is about 2.082, and the confidence interval for the population proportion is
That is,
0.4 +/- 2.082* √[(0.4*0.6)/150]
= 0.4 +/- 0.0833
= (0.3167, 0.4833)
= (31.7%, 48.3%)
Answer: The 96% confidence interval is about (32% to 48%)
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Step 1. Use the binomial square formula:
Applying this formula to the first binomial squared:
Step 2. Apply the formula for the square of a binomial to the second binomial:
In this case, we have some operations to solve before we move on to isolating x. So we solve the operations:
Step 3. Move the terms that are not x squared to the right side of the expression. Remember that when we move one term from one side of the equation to the other, the term must change its sign. We get the following:
Step 4. Combine like terms and arrange terms in order from the greatest exponent to the lowest and leave the independent term at the end:
And that is the final result, which is option A.
Answer: Option A.