Answer:
a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )
d. z= 1.3322
Step-by-step explanation:
We formulate our hypothesis as
a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )
According to the given conditions
p`= 31/225= 0.1378
np`= 225 > 5
n q` = n (1-p`) = 225 ( 1- 31/225)= 193.995> 5
p = 0.4 x= 31 and n 225
c. Using the test statistic
z= p`- p / √pq/n
d. Putting the values
z= 0.1378- 0.11/ √0.11*0.89/225
z= 0.1378- 0.11/ √0.0979/225
z= 0.1378- 0.11/ 0.02085
z= 1.3322
at 5% significance level the z- value is ± 1.645 for one tailed test
The calculated value falls in the critical region so we reject our null hypothesis H0 : p ≤ 0.11 and accept Ha : p >0.11 and conclude that the data indicates that the 11% of the world's population is left-handed.
The rejection region is attached.
The P- value is calculated by finding the corresponding value of the probability of z from the z - table and subtracting it from 1.
which appears to be 0.95 and subtracting from 1 gives 0.04998
Rational expressions are multiplied and divided the same way numeric fractions are.
3 quarts, because 12 is how many cups you have, and there are 4 cups in a quart. 12/4 is 3, so 3 quarts.
1a) Possible rational roots will be of the form
±{divisor of 10}/{divisor of 4}
Divisors of 10 are {1, 2, 5, 10}
Divisors of 4 are {1, 2, 4}
Then possible rational roots are
{±1/4, ±1/2, ±1, ±5/4, ±2, ±5/2, ±5, ±10}
1b) Your answer is correct.
2) One additional root will be the conjuate of the given complex root.
5 -3i
3) If one root is 5 -√7, another will be 5 +√7. Then your polynomial is
P(x) = (x -(5 -√7))*(x -(5 +√7)) = (x -5)^2 -(√7)^2
P(x) = x^2 -10x +18
A) I believe but you might not want to go with it cause I'm not good at math AT ALL:)