Question

the city wishes to estimate the average commute distance for all city employees. they collect a random sample of 91 employees and find a sample mean of \\(\bar{x} = 8.1\\) miles and standard deviation of \\(s = 1.1\\) miles.

calculate the \\(t\\)-interval to estimate, \\(\mu\\), the average commute distance for all city employees with \\(95\\%\\) confidence.

use the inference for population means tool to answer the following questions.

(a) find the point estimate:

(c) calculate the margin of error:

round to 4 decimal places.

(d) write the interval:

enter the interval without spaces in this format: (x,y) where x and y represent real numbers rounded to 3 decimal places.

Explanation:

Identify the point estimate

Using the Point Estimate knowledge point

$$ \bar{x} = 8.1 $$

Determine the critical value

Using the Critical Value and t-Distribution knowledge points

$$
LATEXBLOCK0
$$

Calculate the margin of error

Using the Margin of Error and Standard Error knowledge points

$$
LATEXBLOCK1
$$

Construct the confidence interval

Using the Confidence Interval knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question (a)

Find the point estimate: <blank>8.1</blank>

Question (c)

Calculate the margin of error: <blank>0.2291</blank>

Question (d)

Write the interval: <blank>(7.871,8.329)</blank>