Asociologist develops a test to measure attitudes towards public transportation and 27 randomly selected subjects are given the test. their mean score is 76.2 and their standard deviation is 21.4. construct the 95% confidence interval for the mean score of all such subjects

The 95% confidence interval for the mean score is:

∈

Step-by-step explanation:

We want to estimate the population mean, that is, the average score of all the subjects.

An estimator for the population mean μ is

Since the sample size is then we use the  statistic    with degrees of freedom

The confidence interval for the mean is:

Where

is the average score of the sample

is the standard deviation of the sample

is the sample size

for a confidence level of 95% and 26 degrees of freedom

Then confidence interval is

∈

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1