A 9 year old boy has $12 saved.

A poll finds that 54% of the 600 people polled favor the incumbent. Shortly after the poll is taken, it is disclosed that the in

Galina-37 [17]

Answer:

The value of z test statistics is 1.561.

Step-by-step explanation:

We are given that a poll finds that 54% of the 600 people polled favor the incumbent.

Shortly after the poll is taken, it is disclosed that the incumbent had an extramarital affair. A new poll finds that 50% of the 1030 polled now favor the incumbent.

Let $p_1$ = population proportion of people who favor the incumbent in the first poll

$p_2$ = population proportion of people who favor the incumbent in the second poll

So, Null Hypothesis, $H_0$ : $p_1\geq p_2$ {means that his support has increased or remained same after the second poll}

Alternate Hypothesis, $H_0$ : $p_1 < p_2$ {means that his support has decreased after the second poll}

The test statistics that would be used here is Two-sample z test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of people who favor the incumbent in first poll = 54%

$\hat p_1$ = sample proportion of people who favor the incumbent in second poll = 50%

$n_1$ = sample of people in first poll = 600

$n_2$ = sample of people in second poll = 1030

So, the test statistics = $\frac{(0.54-0.50)-(0)}{\sqrt{\frac{0.54(1-0.54)}{600}+\frac{0.50(1-0.50)}{1030} } }$

= 1.561

Hence, the value of z test statistics is 1.561.

6 0

2 years ago

Convert this rational number to its decimal form and found to the nearest thousands?

pentagon [3]

Answer:

7 and 1 respectively

Step-by-step explanation:

1/7= 7 ) 1 (, the basic definition of division

7 0

2 years ago

HELP!!! URGENT!!! I WILL GIVE BRAINLEIST THING

lisov135 [29]

Answer:

Horizontal distance = 0 m and 6 m

Step-by-step explanation:

Height of a rider in a roller coaster has been defined by the equation,

y = $\frac{1}{3}x^{2}-2x+8$

Here x = rider's horizontal distance from the start of the ride

i). $y=\frac{1}{3}x^{2}-2x+8$

$=\frac{1}{3}(x^{2}-6x+24)$

$=\frac{1}{3}[x^{2}-2(3x)+9-9+24]$

$=\frac{1}{3}[(x^{2}-2(3x)+9)+15]$

$=\frac{1}{3}[(x-3)^2+15]$

$=\frac{1}{3}(x-3)^2+5$

ii). Since, the parabolic graph for the given equation opens upwards,

Vertex of the parabola will be the lowest point of the rider on the roller coaster.

From the equation,

Vertex → (3, 5)

Therefore, minimum height of the rider will be the y-coordinate of the vertex.

Minimum height of the rider = 5 m

iii). If h = 8 m,

$8=\frac{1}{3}(x-3)^2+5$

$3=\frac{1}{3}(x-3)^2$

(x - 3)² = 9

x = 3 ± 3

x = 0, 6 m

Therefore, at 8 m height of the roller coaster, horizontal distance of the rider will be x = 0 and 6 m

6 0

2 years ago

It takes 8 people to clear an acre of weeds in 4 hours. How many acres can 16 people clear in 4 hours? How many acres can 2 peop

Stella [2.4K]

It will take 2 hours for 16 people to clear an acre of weeds, and 8 hours for 2 people to clear an acre of weeds.

5 0

3 years ago

Clare is painting some doors that are all the same size. She used 2 liters of paint to cover 1 3/5 doors. How many liters of pai

barxatty [35]

Answer:

$1\frac{1}{4}\ liters$

Step-by-step explanation:

step 1

Convert mixed number to an improper fraction

$1\frac{3}{5}=\frac{1*5+3}{5}=\frac{8}{5}$

step 2

Using proportion

$\frac{2}{(8/5)}\frac{liters}{doors} =\frac{x}{1}\frac{liters}{door}\\ \\x=2/(8/5)\\ \\x=10/8\ liters$

step 3

Convert to mixed number

$\frac{10}{8}\ liters=\frac{8}{8}+\frac{2}{8}=1\frac{1}{4}\ liters$

8 0

3 years ago