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
Karolina [17]
3 years ago
9

What is your favorite color? A larger survey of countries, including the United States, China, Russia, France, Turkey, Kenya, an

d others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color. Suppose a random sample of n = 75 college students were surveyed and x = 19 of them said that blue is their favorite color. Does this information imply that the proportion of college students who prefer blue differs from that of the general population? Use ???? = 0.05.
Mathematics
1 answer:
prohojiy [21]3 years ago
7 0

Answer:

z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264  

p_v =2*P(z>0.264)=0.792  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of students said that blue is their favorite color is not different from 0.24

Step-by-step explanation:

Data given and notation

n=75 represent the random sample taken

X=19 represent the students said that blue is their favorite color

\hat p=\frac{19}{75}=0.253 estimated proportion of  students said that blue is their favorite color

p_o=0.24 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

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 true proportion is different from 0.24.:  

Null hypothesis:p=0.24  

Alternative hypothesis:p \neq 0.24  

When we conduct a proportion test we need to use the z statisitc, 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{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264  

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=0.05. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

p_v =2*P(z>0.264)=0.792  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of students said that blue is their favorite color is not different from 0.24

You might be interested in
Write a negative integer and a positive integer whose sum is -3.
Pani-rosa [81]
(-6) + 3 = -3 ;
The negative integer is -6; the positive integer is 3.
3 0
3 years ago
Read 2 more answers
Can someone help me
mr Goodwill [35]
X=4
cross multiply
3x=12
x=4
7 0
3 years ago
Read 2 more answers
Which question is best for gathering statistics?
Yakvenalex [24]

Answer: A

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Write the phrase as an expression. Then evaluate when y=20.
alisha [4.7K]

Answer:

Q=\frac{40}{y-16}

Q=10

Step-by-step explanation:

Let the quotient be represented by 'Q'.

Given:

The difference of a number 'y' and 16 is y-16

Quotient is the answer that we get on dividing two terms. Here, the first term is 40 and the second term is y-16. So, we divide both these terms to get an expression for 'Q'.

The quotient of 40 and y-16 is given as:

Q=\frac{40}{y-16}

Now, we need to find the quotient when y=20. Plug in 20 for 'y' in the above expression and evaluate the quotient 'Q'. This gives,

Q=\frac{40}{20-16}\\Q=\frac{40}{4}=10

Therefore, the quotient is 10, when the value of 'y' is 20.

7 0
3 years ago
What is the solution to the inequality shown below?
lesantik [10]

To solve the inequality, you need to isolate/get the variable "p" by itself in the inequality:

5p + 26 < 72           Subtract 26 on both sides

5p + 26 - 26 < 72 - 26

5p < 46      Divide 5 on both sides to get "p" by itself

\frac{5p}{5}

p

p < 9.2       Your answer is A

8 0
3 years ago
Other questions:
  • Solve the inequality 2x&lt;2 pleaseeeeeeeeeeeeee
    9·1 answer
  • Rewrite the equation 4x + 5x2 = 8x – 7 in standard form and
    10·1 answer
  • The percentage of students who attended the talent show for years 2018 to 2013 I shown year | percent of students 2008 | 83% 200
    13·1 answer
  • Can someone please help me!?
    15·2 answers
  • If f=(x)=7(x-1)+8, what is the value of f(1)?
    15·1 answer
  • On an algebra quiz, Alice got 24 problems correct and 4 incorrect. What is the ratio of correct problems to the total number of
    12·1 answer
  • 40 - 2x [(8 x 3 + 6) +<br>12 -2 pls answer correctly​
    14·2 answers
  • I’ll give brainleist!! Help me please i need the answer right now
    6·1 answer
  • Please help lol LOL lol
    6·2 answers
  • Type a digit that makes this statement true.<br> 48,49 ,867 is divisible by 9.<br> Submit
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!