1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
djyliett [7]
3 years ago
11

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. Compute 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.
Mathematics
1 answer:
alexdok [17]3 years ago
7 0

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 = <u><em>population proportion of cars driven at high altitudes who exceeded a standard of 10 grams</em></u>.

p_2 = <u><em>population proportion of cars driven at low altitudes who exceeded a standard of 10 grams</em></u>.

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 <u>Two-sample z-test statistics</u> 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.

You might be interested in
Jodi poured herself a cold soda that had an initial temperature 36 degrees F and immediately went outside to sunbathe where the
mr Goodwill [35]

this can be solve using newtons heating of cooling

(Ts – T) =(Ts – To)*e^(-kt)

Where Ts is the ambient temperature

To is initial temperature

T is the temperature at time t

t is the time

k is constant

fisrt solve the constant k for the given first scenario

(99 – 36) = (99 – 46)*e(-5k)

K = -0.0346

Using k, solve T at t = 13 min

(99 – 46) = (99 – T)*e(-13*(-0.0346)

T = 58.82 degree F

4 0
3 years ago
Regina bought food for her family. She bought 31/2 pounds of oranges and 33/4 pounds of peaches if she used all but 13/8 pounds
Llana [10]

3 \frac{1}{2} + 3 \frac{3}{4} = 3 \frac{2}{4} + 3 \frac{3}{4} = 6 \frac{1}{4}  \: is \: the \: total \: amount \: of \: fruit \\  \\ 6 \frac{1}{4} - 1 \frac{3}{8} = 6 \frac{2}{8} - 1 \frac{3}{8} =  \frac{50}{8} -  \frac{11}{8} =  \frac{39}{8} = 4 \frac{7}{8} \: is \: the \: amount \: of \: fruit \: in \: the \: salad
8 0
3 years ago
Keith plans to buy a car in the future.He currently has $3000 saved up to buy a car. How much money does he need to save per mon
Brut [27]

Answer:

about $709 per month

Step-by-step explanation:

Okay, so in order to solve this question, we should follow this formula:

3,000 + 24x \geq 20,000

where 24 is the amount of time we have and x is the variable we are using as to show the unknown amount of money earned per month.

3,000 + 24x \geq 20,000

-3,000               -3,000

24x \geq 17,000

/24           /24

x \geq approximately 709 dollars

so, we substitute x for 709

3,000 + 24(709) \geq 20,000

3,000 + 17,016 \geq 20,000

20,016 \geq 20,000

which is true

Hope this helps :)

3 0
2 years ago
A paper popcorn cone measures 4 inches in a diameter and is 9 inches high?
Aloiza [94]

Explanation is in the file

tinyurl.com/wtjfavyw

8 0
3 years ago
Read 2 more answers
Bruh, who else has exams?
Llana [10]

Answer:

I have exams too well cba's

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • What is the answer for part a and b
    10·1 answer
  • How many boxes are shipped
    12·2 answers
  • Emily has $15 to buy apples. Apples
    12·1 answer
  • A board 125 centimeters long is cut into 12 pieces of equal length . What is the length of each piece , to the nearest tenth of
    7·1 answer
  • True or false someone help me plzzzzz I’m going to fail !
    8·2 answers
  • Want to learn symmetry?<br>​
    15·2 answers
  • 6.
    13·1 answer
  • The values of x and y vary directly write an equation that relates x and y x = 0.1 y = 0.9
    12·1 answer
  • What is square root of 5x^4-6x^5+x^6+16x^3-8x^2-8x+4 ? <br>help me pleasee !​
    6·1 answer
  • A company sells their product in Canada and the United States. They wonder if people in both countries will respond similarly to
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!