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
Charra [1.4K]
3 years ago
7

Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the pre

vious 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased; what is the critical value
Mathematics
1 answer:
artcher [175]3 years ago
6 0

Answer: The proportion of new car buyers that trade in their old car has statistically significantly decreased.

Step-by-step explanation:

Since we have given that

p = 48% = 0.48

n = 115

x = 46

So, \hat{p}=\dfrac{46}{115}=0.40

So, hypothesis would be

H_0:\ p=\hat{p}\\\\H_a:p

So, test value would be

z=\dfrac{p-\hat{p}}{\sqrt{\dfrac{p(1-p)}{n}}}\\\z=\dfrac{0.48-0.40}{\sqrt{\dfrac{0.48\times 0.52}{115}}}\\\\z=\dfrac{0.08}{0.0466}\\\\z=1.72

At 10% level of significance, critical value would be

z= 1.28

Since 1.28 < 1.72

So, we will reject the null hypothesis.

Hence, the proportion of new car buyers that trade in their old car has statistically significantly decreased.

You might be interested in
1/8(−8c+16)−1/3(6+3c)
Art [367]

Answer:

hope this helps (look in the picture)

Step-by-step explanation:

8 0
3 years ago
Write an equation of the perpendicular bisector of the segment with end points M(1,5) and N(7,-1)
vitfil [10]
The perpendicular bisector of the segment passes through the midpoint of this segment. Thus, we will initially find the midpoint P:

P=\dfrac{(1,5)+(7,-1)}{2}=\dfrac{(8,4)}{2}=(4,2)

Now, we will calculate the slope of the segment support line (r). After this, we will use the fact that the perpendicular bisector (p) is perpendicular to r:

m_r=\dfrac{\Delta y}{\Delta x}=\dfrac{5-(-1)}{1-7}=\dfrac{6}{-6}\iff m_r=-1


p\perp r\Longrightarrow m_p\cdot m_r=-1\Longrightarrow m_p\cdot(-1)=-1\iff m_p=1

We can calculate the equation of p by using its slope and its point P:

y-y_P=m_p(x-x_P)\\\\&#10;y-2=1\cdot(x-4)\\\\&#10;y-2=x-4\\\\&#10;\boxed{p:~~y=x-2}
4 0
3 years ago
Pls help asap for brainiest answer!
gizmo_the_mogwai [7]

Answer:

Quest 1. is C, i.e 8. besides thier base are equal.

Quest 2. is D

Wuest 3. is C

6 0
3 years ago
To compare two programs for training industrial workers to perform a skilled job, 20 workers are included in an experiment. Of t
nikklg [1K]

Answer:

t=\frac{19.1-23.3}{\sqrt{\frac{4.818^2}{10}+\frac{5.559^2}{10}}}}=-1.805  

p_v =P(t_{(18)}

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude the the true mean for method 1 is lower than the mean for the method 2 at 5% of significance

Step-by-step explanation:

Data given and notation

We can calculate the sample mean and deviation with these formulas:

\bar X = \frac{\sum_{i=1}^n X_i}{n}

s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

\bar X_{1}=19.1 represent the mean for the sample mean for 1

\bar X_{2}=23.3 represent the mean for the sample mean for 2

s_{1}=4.818 represent the sample standard deviation for the sample 1

s_{2}=5.559 represent the sample standard deviation for the sample 2

n_{1}=10 sample size selected 1

n_{2}=10 sample size selected 2

\alpha represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

p_v represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the average time taken when training under method 1 is less than the average time for Method 2, the system of hypothesis would be:

Null hypothesis:\mu_{1} \geq \mu_{2}

Alternative hypothesis:\mu_{1} < \mu_{2}

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}} (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

t=\frac{19.1-23.3}{\sqrt{\frac{4.818^2}{10}+\frac{5.559^2}{10}}}}=-1.805  

P-value

The first step is calculate the degrees of freedom, on this case:

df=n_{1}+n_{2}-2=10+10-2=18

Since is a one sided test the p value would be:

p_v =P(t_{(18)}

Conclusion

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude the the true mean for method 1 is lower than the mean for the method 2 at 5% of significance

4 0
2 years ago
Simplify the algebraic expression:<br><br> 2(y + 5) + 3y - 4
love history [14]

Answer:

2y +10 +3y-4

5y+6

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • Tammy buys a 4-gigabyte memory card for her camera. Dijonea buys a memory card with twice as much storage as Tammy’s. One gigaby
    11·1 answer
  • Analyze the diagram below and answer the question that follows.
    13·1 answer
  • How was basic math used
    7·2 answers
  • A wooden flooring strip is 20 1/2 inches long. If you cut off 4 3/4 inches from one end what will be the new length of the strip
    9·1 answer
  • A rectangle a photo with dimension 3 inches wide by 4 inches long is enlarged to a length of 12 inches what is the width of the
    15·1 answer
  • Use the square root property to solve the Quadratic Equation.<br> x2 = -49
    7·2 answers
  • PLEASE HELPPPPPP!!!!!!Solve this system of linear equations separate the x-and y-values with a comma
    15·1 answer
  • Use substitution to solve the system.<br> -5x + 3y = 19<br> x = 3y - 11
    13·1 answer
  • 12 The points (-15, -3) and (-7, -1) both lie
    15·1 answer
  • Pythagorean Theorem with Known Legs
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!