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
Agata [3.3K]
3 years ago
12

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 can you conclude concerning the null hypothesis?
Mathematics
1 answer:
choli [55]3 years ago
4 0

Answer:

z=\frac{0.4 -0.48}{\sqrt{\frac{0.48(1-0.48)}{115}}}=-1.717  

p_v =P(z  

So the p value obtained was a very low value and using the significance level given \alpha=0.1 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people that have traded in their old car is lower than 0.48 or 48%.  

Step-by-step explanation:

Data given and notation

n=115 represent the random sample taken

X=46 represent the number of people that have traded in their old car.

\hat p=\frac{46}{115}=0.4 estimated proportion of people that have traded in their old car

p_o=0.48 is the value that we want to test

\alpha=0.1 represent the significance level

Confidence=90% or 0.9

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion is less than 0.48.:  

Null hypothesis:p\geq 0.48  

Alternative hypothesis:p < 0.48  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.4 -0.48}{\sqrt{\frac{0.48(1-0.48)}{115}}}=-1.717  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.1. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(z  

So the p value obtained was a very low value and using the significance level given \alpha=0.1 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people that have traded in their old car is lower than 0.48 or 48%.  

You might be interested in
My goal was to raise $5,000 to help protect the manatees. She raised 3,500. What percent of her goal did she achieve
Oxana [17]

3500 is about 70% of 5000

8 0
3 years ago
What is the area of the figure below? The figure shows a parallelogram. the left side equals 5 inches. The bottom side equals 12
Strike441 [17]

Answer:

A = 36 in.²

Step-by-step explanation:

The area of a parallelogram can be determined by the formula:

A = bh

The base length is 12 inches and the height is 3 inches.

A = 12in. * 3in.

A = 36 in.²

5 0
3 years ago
Which inequality statement best represents the graph below?
joja [24]
A would be the most accurate choice. This is because the shading is above the parabola indicating it’s solutions are greater. And it’s not a positive parabola
4 0
3 years ago
There's a plane that flies at an altitude of 25,000 feet. There's a submarine that dives to a depth of 600 feet below sea level.
ella [17]
25,000 + 600 considering they would meet at 0, so they are 25,600 feet apart
8 0
3 years ago
A farmer sells 8.7 kilograms of pears and apples at the farmer's market. 2 5 of this weight is pears, and the rest is apples. Ho
Ivenika [448]

Answer: 5.22kg

Step-by-step explanation:

From the question, a farmer sells 8.7 kilograms of pears and apples at the market. Of the pears and apples sold, 2/5 of this weight is pears, and the rest is apples. To calculate the kilograms of apple sold goes thus:

Total kilograms sold = 8.7kg

Fraction of pears weight = 2/5

Pears kilograms sold = 2/5 × 8.7

= 0.4 × 8.7

= 3.48kg

Since the kilograms of pears sold is , 3.48kg, to get the kilograms of apple sold, we subtract 3.48kg from 8.7kg. This will be:

= 8.7kg - 3.48kg

= 5.22kg

8 0
3 years ago
Other questions:
  • What is the value of the expression 8p4
    5·1 answer
  • In calculating the bank discount when discounting an interest-bearing note, which one of the following is not used in the calcul
    15·1 answer
  • In how many ways can four aces be drawn from a deck of cards? (Order is not important.)
    9·1 answer
  • How to change one third into twelfths
    7·2 answers
  • What am I supposed to do
    5·2 answers
  • Suppose that y varies directly with x and y = 10 when x = 20. What is y when x = 15?
    15·1 answer
  • Find the slope and the y-intercept of the graph of y=−45x−2.
    11·1 answer
  • Which ones are linear ? <br> please help thanks
    7·1 answer
  • G.SRT.B.5 Worksheet #2
    13·1 answer
  • What is the phenotypic ratio of the offspring? 1:1:1:1:2:2:2:2:4 1:3:3:9 1:4 4:12
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!