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.
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.
(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.
(b)Confidence interval for the population proportion:
The (1-α) % confidence interval for proportion p is given by,
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