- the number of green blocks which is equal to the number of favourable events
- the number of all blocks, which is equal to the number of all possible outcomes
Answer:
Since the calculated value of z= -1.496 does not fall in the critical region z < -1.645 we conclude that the new program is effective. We fail to reject the null hypothesis .
Step-by-step explanation:
The sample proportion is p2= 7/27= 0.259
and q2= 0.74
The sample size = n= 27
The population proportion = p1= 0.4
q1= 0.6
We formulate the null and alternate hypotheses that the new program is effective
H0: p2> p1 vs Ha: p2 ≤ p1
The test statistic is
z= p2- p1/√ p1q1/n
z= 0.259-0.4/ √0.4*0.6/27
z= -0.141/0.09428
z= -1.496
The significance level ∝ is 0.05
The critical region for one tailed test is z ≤ ± 1.645
Since the calculated value of z= -1.496 does not fall in the critical region z < -1.645 we conclude that the new program is effective. We fail to reject the null hypothesis .
Continuous compounding is the mathematical limit that compound interest can reach.
It is the limit of the function A(1 + 1/n) ^ n as n approaches infinity. IN theory interest is added to the initial amount A every infinitesimally small instant.
The limit of (1 + 1/n)^n is the number e ( = 2.718281828 to 9 dec places).
Say we invest $1000 at daily compounding at yearly interest of 2 %. After 1 year the $1000 will increase to:-
1000 ( 1 + 0.02/365)^365 = $1020.20
with continuous compounding this will be
1000 * e^1 = $2718.28
Answer A. is correct I’m pretty sure
