In a random sample of 27 people, the mean commute

Ответ:

Bloom247

23.01.2022

The 95% CI is

$27.5\leq \mu \leq 33.3$

The margin of error is 2.9 minutes.

Step-by-step explanation:

The question is incomplete:

The sample standard deviation was 7.3 minutes.

Assume the population is normally distributed and use a t-distribution to construct a 95% confidence interval for the population mean mu.

The sample mean is 30.4

The sample standard deviation is 7.3

The sample size is 27.

The degrees of freedom are:

df=n-1=27-1=26

For a 95% CI and df=26, the critical value for t is t=2.056.

The margin of error can be calculated as:

$E=t\cdot s/\sqrt{n}=2.056*7.3/\sqrt{27}=15/5.2=2.9$

The lower and upper bounds of the 95% CI are:

$LL=\bar x-t\cdot s/\sqrt{n}=30.4-2.9=27.5\\\\UL=\bar x+t\cdot s/\sqrt{n}=30.4+2.9=33.3$

The 95% CI is then

$27.5\leq \mu \leq 33.3$

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