-8/9 * 2/5 I can't figure it out -

In a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per

alexdok [17]

Answer:

The test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard is 3.234.

Step-by-step explanation:

We are given that in a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed.

In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard.

Let $p_1$ = population proportion of cars driven at high altitudes who exceeded a standard of 10 grams.

$p_2$ = population proportion of cars driven at low altitudes who exceeded a standard of 10 grams.

So, Null Hypothesis, $H_0$ : $p_1\leq p_2$ {means that the proportion of high-altitude vehicles exceeding the standard is smaller than or equal to the proportion of low-altitude vehicles exceeding the standard}

Alternate Hypothesis, $H_A$ : $p_1>p_2$ {means that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard}

The test statistics that will be used here is Two-sample z-test statistics 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 cars driven at high altitudes who exceeded a standard of 10 grams = $\frac{24}{90}$ = 0.27

$\hat p_2$ = sample proportion of cars driven at low altitudes who exceeded a standard of 10 grams = $\frac{42}{380}$ = 0.11

$n_1$ = sample of cars driven at high altitudes = 90

$n_2$ = sample of cars driven at low altitudes = 380

So, the test statistics = $\frac{(0.27-0.11)-(0)}{\sqrt{\frac{0.27(1-0.27)}{90}+\frac{0.11(1-0.11)}{380} } }$

= 3.234

The value of z-test statistics is 3.234.

7 0

3 years ago

What is the area of the following circle? the radius is 1 unit

Brilliant_brown [7]

Answer:

The area is π= 3.14 approx

Hope it helps!

Step-by-step explanation:

Area of circle = πr^2

Radius= r = 1 unit

So area,

= 3.14*(r)^2

= 3.14*(1)^2

= 3.14*1

= 3.14 or π if you want the specific answer

6 0

3 years ago

Read 2 more answers

9. The temperature outside Jeff's house is 14 °C at midday.

velikii [3]

Answer:

-13ºC

Step-by-step explanation:

The temperature has fallen, so you subtract.

14ºC-27ºC=-13ºC

7 0

3 years ago

Adidea Corp regularly buts merchandise from vendors. It just purchased 1,000 units on credit from one of its vendors. How will t

Lostsunrise [7]

Answer:

You did not include the price they bought the units at.

I will assume this price is $5.

= 5 * 1,000

= $5,000

Recording it will be:

Account Debit Credit

Merchandise Inventory $5,000

Accounts Payable $5,000

7 0

3 years ago

How to solve the equations

Arada [10]

So first off, we need to establish that there are three terms that we need to find: a, c & E.

Let's write the three equations below:

Equation No. 1 -
a + c - 2E = 2

Equation No. 2 -
a - 2c = 5

Equation No. 3 -
- c + E = 4

To begin working out our answer, we will make (a) the subject of our second equation & (E) the subject of the third equation so that we can substitute them into the first equation as displayed below:

Equation No. 2 -
a - 2c = 5
a = 5 + 2c

Equation No. 3 -
- c + E = 4
E - c = 4
E = 4 + c

From there, we substitute the given equations for (a) & (E) into the first equation in order to make (c) the subject in the first equation as displayed below:

Equation No. 1 -
a + c - 2E = 2
( 5 + 2c ) + c - 2 ( 4 + c ) = 2
5 + 3c - 8 - 2c = 2
3c - 2c = 2 - 5 + 8
c = 5

Extending from this, by substituting the value of c, which is 5, into Equation No. 2 & 3, we will be able to also obtain the values of both (a) & (E) as displayed below:

Equation No. 2 -
a = 5 + 2c
a = 5 + 2 ( 5 )
a = 5 + 10
a = 15

Equation No. 3 -
E = 4 + c
E = 4 + ( 5 )
E = 9

Therefore, we have now successfully found the values of a, c & E as displayed below:

a = 15
c = 5
E = 9

If you want to check your answer, then simply substitue the values into Equation No. 1. If after solving the equations, the left-hand & right-hand side are equivalent, then the answer is correct. However, if it isn't equivalent, then the answer is either incorrect or you have made an error while solving thr equation. Here is the working out to check your answer for this question:

a + c - 2E = 2
( 15 ) + ( 5 ) - 2 ( 9 ) = 2
20 - 18 = 2
2 = 2

Therefore, the solution is correct.

7 0

4 years ago

-8/9 * 2/5 I can't figure it out -_- Please help!!