Question

A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed. $3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00 Find the 95% confidence interval for the true mean. (Be sure to indicate your calculations for mean and standard deviation)

Answer 1

The 95% confidence interval for the true mean would be between 3.39 and 6.01

Step-by-step explanation:

In order to calculate the 95% confidence interval for the true mean we would have to calculate first the mean and standard deviation as follows:

mean=∑Xi/n

mean=$3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00/10

mean=4.7

standard deviation=√∑(Xi-mean)∧2/n-1

standard deviation=1.83

t critical=2.262

The confidence interval=mean +/- t critical*standard deviation/√10

The confidence interval=4.7 +/- 2.262*1.8338/√10

The confidence interval=(3.39, 6.01)

The 95% confidence interval for the true mean would be between 3.39 and 6.01