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
Elanso [62]
3 years ago
11

A car company claims that its new car, the GoFast2000, has a gas mileage of 35 miles per gallon ( mpg ). A consumer group suspec

ts that the true mean gas mileage of the new cars is less than 35 mpg . The group tests 50 randomly selected Go Fast 2000 cars and finds a sample mean of 34.8 mpg . With all assumptions for inference met, a hypothesis test resulted in a p -value of 0.324.
State the null and alternative hypothesis needed to conduct this test. What test statistic should be used and why? Should any assumption be made about the distribution of MPG? What conclusion can be drawn from the sample results? Test at 0.05 level of significance.
Mathematics
1 answer:
I am Lyosha [343]3 years ago
6 0

Answer:

<em>H₀</em>: <em>μ</em> = 35 mpg vs. <em>Hₐ</em>: <em>μ</em> < 35 mpg.

A <em>t</em>-test statistic should be used.

The company's claim is correct.

The true mean gas mileage of the new cars is 35 mpg.

Step-by-step explanation:

The consumer group can perform a test for single mean to determine whether the is less than 35 mpg or not.

The hypothesis can be defined as follows:

<em>H₀</em>: The true mean gas mileage of the new cars is 35 mpg, i.e. <em>μ</em> = 35 mpg.

<em>Hₐ</em>: The true mean gas mileage of the new cars is less than 35 mpg, i.e. <em>μ</em> < 35 mpg.

The information provided is:

<em>n</em> = 50

\bar x = 34.8 mpg

As there is no information abut the population standard deviation then we would have to compute the sample standard deviation to estimate the value of <em>σ</em>.

Since the sample standard deviation will be used, a <em>t</em> test statistic would have to be computed.

The test statistic is given by:

t=\frac{\bar x-\mu}{s/\sqrt{n}}

Assumptions for one sample <em>t</em>-test are:

  • Independent samples
  • The population is normally distributed
  • The sample size should be large enough to make the assumption of normality.

The significance level of the test is, <em>α</em> = 0.05.

The <em>p</em>-value of the test is 0.324.

The decision rule based on <em>p</em>-value is that the null hypothesis will be rejected if the <em>p</em>-value is less than the level of significance and vice-versa.

The <em>p</em>-value = 0.324 > <em>α</em> = 0.05.

As the <em>p</em>-value is more than the significance level the null hypothesis will not be rejected.

Thus, concluding that the company's claim is correct.

The true mean gas mileage of the new cars is 35 mpg.

You might be interested in
your mother gave you 14.28 with which to buy a present. this covered 3/4 of the cost. how much did the present cost?
saul85 [17]

$19.04. If your mom gave you $14.28, and it only covered 3/4 of the cost, you have to first find 3/4 as a percentage, and then put it into a decimal. It would be 0.75. So then you have to divide 14.28÷0.75. It turns out to be $19.04.

8 0
3 years ago
What is the solution to the system of equations? -2x + y = -5 3x – 2y = 12 A) (3, 1) B) (6, 3) C) (-2, -9) D) (-2, -1)
max2010maxim [7]

Answer:

The correct answer is D) (-2, -1)

Step-by-step explanation:

In order to solve this system of equations, start by multiplying the entire first equation by 2. Then add the two equations together. This will get the y's to cancel and allow you to solve for x.

-4x + 2y = -10

3x - 2y = 12

---------------------

-x = 2

x = -2

Now that we have the value for x, we can find y by plugging the x value into either equation.

-2x + y = -5

-2(2) + y = -5

-4 + y = -5

y = -1

6 0
3 years ago
Earth, Mars, Saturn, Uranus and Neptune revolve around the sun. Earth takes 1 year, Mars 2 years, Saturn 30 years, Uranus 84 yea
Anettt [7]

Answer:

  30 years

Step-by-step explanation:

2 is a factor of 30, so the LCM of 2 and 30 is 30.

Saturn and Mars will appear in the same direction in the night sky every 30 years.

3 0
3 years ago
6 for $14.34<br> each. Please I really need help with this.
Marrrta [24]
6 items for $14.34 each is $86.04.
3 0
3 years ago
Find the first, fourth, and eighth terms of the sequence. A(n) = –3 • 2^n–1
Sphinxa [80]
A(n) = –3 • 2⁽ⁿ⁻¹⁾

for n = 1 ,  A₁ = -3.(2)⁰ = -3
for n = 2 ,  A₂ = -3.(2)¹ = -6
for n = 3 ,  A₃ = -3.(2)² = -12
for n = 4 ,  A₄ = -3.(2)³ = -24
...........................................
for n = 8 ,  A₈ = -3.(2)⁷ = -384


4 0
3 years ago
Other questions:
  • The sum of the series shown in the picture
    10·1 answer
  • Can someone help with this question please?
    8·1 answer
  • Lines e and f are parallel. The mAngle9 = 80° and mAngle5 = 55°.
    9·2 answers
  • 32b=8<br> Whats the number for b??
    12·2 answers
  • Which statement is true based on the information given on the coordinate plane select all that apply
    9·1 answer
  • Pls answer all questions
    10·2 answers
  • $16 for 4 books. How much would 12 books cost?
    11·2 answers
  • Vicci designed a square tile in art class. Each corner of the square tile has a measure of 90 degrees. 30° Which equation could
    5·1 answer
  • Consider the inequality.<br> What is the solution to inequality
    8·2 answers
  • one endpoint of a line segment is (1,2) and the midpoint of the midpoint of the segment is (-1,4) what is the other end point ?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!