The city wishes to estimate the average commute distance for all city employees. They collect a random sample of 97 employees and find a sample mean of \overline{x}=7.1 \overline{x}=7.1 miles. Calculate the z interval to estimate, \mu \mu, the average commute distance for all city employees.

UkusakazaL

UkusakazaL

Answered question

2021-08-02

The city wishes to estimate the average commute distance for all city employees. They collect a random sample of 97 employees and find a sample mean of x=7.1x=7.1 miles. They also assume a population standard deviation of σ=1.5σ=1.5 miles. Calculate the z interval to estimate, μμ, the average commute distance for all city employees with 95% confidence.
Round your answers to 2 decimal places.
Find the Critical Value z*:
Point Estimate:
Margin of Error:
Write the interval as (lower bound, upper bound)

Answer & Explanation

Ian Adams

Ian Adams

Skilled2021-08-17Added 163 answers

Step 1
The random variable commute distance for all city employees follow normal distribution.
The sample size is 97.
The sample mean is 7.1.
The population standard deviation is 1.5.
We have to find the 95% confidence interval for the population mean.
We have to use Z-table.
Step 2
From Z-table, the 95% critical value is z=1.96.
Point estimate: 7.1.
ME=z×σn
=1.96×1.597
=0.30
Margin of error: 0.30.
Step 3
CI=x±ME
=7.1±0.30
=(7.10.30,7.1+0.30)
+(6.80,7.40)
The 95% confidence interval is (6.80, 7.40).

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