Answer:
Step-by-sep explanation:
Given:
Diameter of circle = 20 units
Center of circle = (-1, 7)
Standard form of the equation of a circle is expressed in the center-radius form as:
,
Where,
h = -1
k = 7
r = ½ of diameter = ½(20) = 10 units
Plug in the values into the equation
Let be the population mean lifetime of circulated $1 bills.
By considering the given information , we have :-
Since the alternative hypotheses is two tailed so the test is a two tailed test.
We assume that the lifetime of circulated $1 bills is normally distributed.
Given : Sample size : n=50 , which is greater than 30 .
It means the sample is large so we use z-test.
Sample mean :
Standard deviation :
Test statistic for population mean :-
The p-value=
Since the p-value (0.0433834) is greater than the significance level (0.02) , so we do not reject the null hypothesis.
Hence, we conclude that we do not have enough evidence to support the alternative hypothesis that the average lifetime of a circulated $1 bill differs from 18 months.