Question

For each of the following situations, identify the parameter being estimated and calculate anappropriate 95% confidence interval for the parameter. In your own words, interpret the interval.

1. A poll of 700 Americans is taken and they are asked to state their favorite color. 187 of those polled respond that red is their favorite color.

2. Suppose we want to estimate the average weight of an adult male in Dekalb County, Georgia. We draw a random sample of 1,000 men and weight them. We find that the average man in our sample weighs 180 pounds, and the standard deviation of the sample is 30 pounds

Answer 1

(1) Parameter: In the following question the parameter of interest is the true proportion of Americans , i.e., have red color being their favorite color.

In the question we have given that a random sample of Americans has taken and 187 state that their favorite color is red, then the sample proportion is calculated as -

The formula for calculating the confidence interval for the true proportion is given by :

Critical value: For 95% confidence

• So the 95% confidence interval for the true proportion of Americans whose favorite color is red is calculated as , i.e.,

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(2) Parameter: The parametr of interest here is the true average weight of adult male in Dekalb County, i.e.,

Given: sample size, ; sample mean, ; sample standard deviation,

The formula for calculating the confidence interval for the true average weight of the adult male in Dekalb County is given by :

Critcal value: For 95% confidence,

• So the 95% confidence interval for the true mean weight of adult male in Dekalb County is calculated as , i.e.,