Question

In: Statistics and Probability

LED headlights on cars seem to becoming increasingly popular, so I thought I would make my...

LED headlights on cars seem to becoming increasingly popular, so I thought I would make my problem about that. I believe that the proportion of car owners who have LED headlights is higher than the proportion of car owners to use regular non-LED headlights now, (according to data from 2019) versus in 2010. During two independent surveys, one survey noted that 355 out of 600 car owners had LED headlights in 2020, while in 2010, 250 out of 600 car owners had LED headlights.

Test this hypothesis using the significance level of 0.05.

Solutions

Expert Solution

For sample 1, we have that the sample size is N1​=600, the number of favorable cases is X1​=355, so then the sample proportion is

For sample 2, we have that the sample size is N2​=600, the number of favorable cases is X2​=250, so then the sample proportion is

The value of the pooled proportion is computed as

Also, the given significance level is α=0.05.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: ​

Ha: ​

This corresponds to a right-tailed test, for which a z-test for two population proportions needs to be conducted.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a right-tailed test is zc​=1.64.

The rejection region for this right-tailed test is R={z:z>1.64}

(3) Test Statistics

The z-statistic is computed as follows:
(4) The decision about the null hypothesis

Since it is observed that z=6.062>zc​=1.64, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0, and since p=0<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p1​ is greater than p2​, at the 0.05 significance level. Hence the proportion of car owners who have LED headlights is higher than the proportion of car owners to use regular non-LED headlights now, (according to data from 2019) versus in 2010.

Every upvote matters! So please do upvote if you are satisfied! Let me know in the comments if anything is not clear. I will reply ASAP!

orchestra answered 2 years ago
Next > < Previous

Related Solutions

NFP-Government relationships are becoming increasingly popular based: i) NFPs increased in growth and prominence with Government;...
NFP-Government relationships are becoming increasingly popular based: i) NFPs increased in growth and prominence with Government; and ii) Government newfound desire to engage NFPs to implement governmental policies. In your own opinion, discuss this statement and provide reasons for your answer.
How would I make it so that when I run my code it does not ask...
How would I make it so that when I run my code it does not ask for input (not having to enter after the statement and enter 0 for example) after ROXY (Forever ROXY Enterprises) appears? Like it would tell me the second statement right away along with the Roxy phrase. This is in C++. My code: #include / #include using std::endl; int main() {    void readAndConvert();    unsigned int stockSymbol;    unsigned int confNum;    std::cout << "ROXY...
I can't seem to make my inheritance to work properly between my parent class GameCharacter and...
I can't seem to make my inheritance to work properly between my parent class GameCharacter and the child classes hero and villain. Here's my code: import java.sql.SQLOutput; public class Main { public static void main(String[] args) { GameCharacter me = new GameCharacter("King Arthur", 5); GameCharacter tree = new GameCharacter("Tall Tree", 5); GameCharacter enemy = new GameCharacter("Monster Bug", 10); System.out.println(); System.out.println("\n~~~ Game Characters Created ~~~"); System.out.println(tree); System.out.println(me); System.out.println(enemy); System.out.println("\n~~~ The Bug Has Been Attacked ~~~"); me.attack(enemy); System.out.println(tree); System.out.println(me); System.out.println(enemy); System.out.println("\n~~~ The...
I need a short and clear opinion so I can understand the question and make my...
I need a short and clear opinion so I can understand the question and make my own opinion Writing in the 19th century, the British economist Thomas Malthus argued that the law of diminishing marginal returns implied eventual misery for humanity because, in the case of agriculture, there is a fixed amount of available land and additional labor would only yield ever smaller increases in food production. The inevitable result, as Malthus saw it, was that population growth would eventually...
Question1 Consider this statement: Cultures around the world are becoming increasingly similar, so companies should standardize...
Question1 Consider this statement: Cultures around the world are becoming increasingly similar, so companies should standardize both their products and global marketing efforts. Do you agree or disagree with this line of reasoning? Explain. Are there certain industries for which the statement might be more or less true? Question 2 Critics of the tobacco industry allege that in developing markets cigarette manufacturers create special tobacco blends that contain additives to give an extra "kick." If true, such practices put the...
Consider this statement: Cultures around the world are becoming increasingly similar, so companies should standardize both...
Consider this statement: Cultures around the world are becoming increasingly similar, so companies should standardize both their products and global marketing efforts. 1. Do you agree or disagree with this line of reasoning? Explain. 2. Are there certain industries for which the statement might be more or less true?
Consider this statement: Cultures around the world are becoming increasingly similar, so companies should standardize both...
Consider this statement: Cultures around the world are becoming increasingly similar, so companies should standardize both their products and global marketing efforts. 1. Do you agree or disagree with this line of reasoning? Explain. 2. Are there certain industries for which the statement might be more or less true? Your response to each question should be a minimum of 6 sentences long.
Here is my C++ program so far. Is there anyway I can make it display an...
Here is my C++ program so far. Is there anyway I can make it display an error if the user enters a float? Thanks #include <iostream> using namespace std; // Creating a constant for the number of integers in the array const int size = 10; int main() { // Assigning literals to the varibles int a[size]; int sum=0; float avg; // For loop that will reiterate until all 10 integers are entered by the user for(int i=0; i<size; i++)...
okay so i am working on a physic review quetion that i seem not to know...
okay so i am working on a physic review quetion that i seem not to know where to start.. It states as follow A magnetic field of .250T points straight up in a lab, a circular coil of wire with 10 turns, a radius of 12 cm and a resistance of 1.6 ohms, sits on a slanted surface, tilted at 30 degress from horizontal. Then the magnetic field is turn off and it decays exponentially to 0. (B=Boe-t/T) At the...
How would I synthesize m-isopropylbenzoic acid from benzene? My initial thought was to do alkylation and...
How would I synthesize m-isopropylbenzoic acid from benzene? My initial thought was to do alkylation and treat with KMnO to produce the carboxylic acid and then do alkylation to produce the isopropyl at the meta position. But that wouldn’t work, because alkylation and acylation do not occur in the presence of strong or moderate deactivators.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT