3. In a survey of 209 Montana residents, 61 reported their financial status was worse than a year ago.a. Let p be the proportion of the population who responded "yes". Use the given information to find the point of estimate for the population proportion.b. Construct a 90% confidence interval for the population proportion.

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3. In a survey of 209 Montana residents, 61 reported their financial status was worse than a year ago.
a. Let p be the proportion of the population who responded "yes". Use the given information to find the point of estimate for the population proportion.
b. Construct a 90% confidence interval for the population proportion.

 

Expert Solution
Step 1

(a) Computing the point estimate of population proportion:

The point estimate of population proportion, p-hat is defined as, p-hat = x/n, where x is the number of success and n is the size of the sample.

It is given that, in a survey of 209 residents, 61 reported that their financial status was worse than a year ago.

Let x denote the number of residents who responded “Yes”.

That is, the number of trials, n = 209 and number of success, x = 61.

Therefore, the sample proportion p-hat is, 61 / 209 = 0.29.

In other words, the point estimate of population proportion is 0.29.

Step 2

(b)Confidence interval for the population proportion:

The (1-α) % confidence interval for proportion p is given by,

pxq
ptz
n
2
p <p+z,
n
n
x
Here,
n
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