Answer:
Step-by-step explanation:
For the null hypothesis,
µ = 60
For the alternative hypothesis,
h1: µ < 60
This is a left tailed test
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 100,
Degrees of freedom, df = n - 1 = 100 - 1 = 99
t = (x - µ)/(s/√n)
Where
x = sample mean = 52
µ = population mean = 60
s = samples standard deviation = 22
t = (52 - 60)/(22/√100) = - 3.64
We would determine the p value using the t test calculator. It becomes
p = 0.00023
We would reject the null hypothesis if α = 0.05 > 0.00023
4 thousands equals 40 hundreds.
Answer:
They need to survey 4145 residents.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of 
.
The margin of error is given by:
99% confidence level
So 
, z is the value of Z that has a p-value of 
, so 
.
At least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.02 of the true proportion?
This is n for which 
. As we have no estimate for the proportion, we use 
. So
Rounding up:
They need to survey 4145 residents.
