A large poll showed that 42%, percent of adults approved of their nation's prime minister. Margot wants to test if it is now lower, so she takes a random sample of 1,000 adults in that nation and finds that 390—or 39% percent of those sampled—approved of the prime minister. Let p represent the proportion of adults in this nation who approve of the prime minister.

Which of the following is an appropriate set of hypotheses for her significance test?

Choose 1

(Choice A)
A
\begin{aligned} &H_0: p = 0.39 \\ &H_\text{a}: p < 0.39 \end{aligned}


H
0

:p=0.39
H
a

:p<0.39


(Choice B)
B
\begin{aligned} &H_0: p = 0.39 \\ &H_\text{a}: p < 0.42 \end{aligned}


H
0

:p=0.39
H
a

:p<0.42


(Choice C)
C
\begin{aligned} &H_0: p = 0.42 \\ &H_\text{a}: p < 0.39 \end{aligned}


H
0

:p=0.42
H
a

:p<0.39


(Choice D)
D
\begin{aligned} &H_0: p = 0.42 \\ &H_\text{a}: p < 0.42 \end{aligned}


H
0

:p=0.42
H
a

:p<0.42

According to the situation described, the appropriate set of hypotheses for her significance test is given by:

.

.

At the null hypothesis, it is tested if the proportion is still of 42%, that is:

.

At the alternative hypothesis, it is tested if the proportion is now lower, that is:

.

Hence, the the appropriate set of hypotheses for her significance test is given by:

.

.

More can be learned about an hypothesis test at

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

The solution is in the following image

The answer is in the image 

The answer is in the image 

The solution is given in the image below

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students