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
Gnom [1K]
3 years ago
14

According to a Pew Research Center study, in May 2011, 38% of all American adults had a smart phone (one which the user can use

to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 366 community college students at random and finds that 160 of them have a smart phone. Then in testing the hypotheses: H 0 : p = 0.38 versus H a : p > 0.38, what is the test statistic? z = . (Please round your answer to two decimal places.)
Mathematics
1 answer:
NikAS [45]3 years ago
8 0

Answer:

z=\frac{0.437 -0.38}{\sqrt{\frac{0.38(1-0.38)}{366}}}=2.25  

p_v =P(Z>2.25)=0.012  

Step-by-step explanation:

1) Data given and notation

n=366 represent the random sample taken

X=160 represent the people with smartphones

\hat p=\frac{160}{366}=0.437 estimated proportion of people with smartphones

p_o=0.38 is the value that we want to test

\alpha represent the significance level

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion of people with smatrphones is higher than 0.38:  

Null hypothesis:p \leq 0.38  

Alternative hypothesis:p > 0.38  

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.

3) Calculate the statistic  

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

z=\frac{0.437 -0.38}{\sqrt{\frac{0.38(1-0.38)}{366}}}=2.25  

4) 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 assumed is \alpha=0.05. The next step would be calculate the p value for this test.  

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

p_v =P(Z>2.25)=0.012  

So the p value obtained was a very low value and using the significance level assumed \alpha=0.05 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 true proportion of people with smatphones is higher than 0.38.  

You might be interested in
Solve the inequality ||x-4|-2|<3
Shkiper50 [21]

Answer: Solve the inequality:

||x-4|-2|<3

Step-by-step explanation:Solve the inequality ||x-4|-2|<3

4 0
3 years ago
What does 3 over 8 simplify to
nirvana33 [79]
To simplify, we need to find a number that can divide both the numerator and denominator equally. Can you find a number that will do this? I can't. So it is already simplified.
4 0
3 years ago
Jerry bought 4.2 lbs of jelly beans for $3.98 per lb. Sales tax is 6%. What was the total amount Jerry paid for the jelly beans?
Illusion [34]

Answer:

4.2 x 3.98 = 16.716

6% Sales tax = 1.06

16.716 x 1.06

About 17.72

4 0
3 years ago
How do you solve for x? 3 + 2x = 4y​
Dimas [21]

Answer:

x= 2y - 3/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

8 0
3 years ago
Read 2 more answers
Calculate the area and perimeter plz help
kramer

Answer:

Figure 1:

Area: 30m^2

Perimeter: 23.6m

Figure 2:

Area: 98.8km^2

Perimeter:56.5km

Step-by-step explanation:

Area is base x height.

To get the perimeter, add up all the sides.

Figure 1:

Area:

6x5=30m^2

Perimeter: 6+5.8+6+5.8=23.6m

Figure 2:

Area:

7.6x13 = 98.8km^2

Perimeter:7.6+15+20+13.9=56.5km

7 0
3 years ago
Other questions:
  • Wat is the value of digit 8 in 686,293
    14·2 answers
  • Here are the two arguments you will be debating: Argument A: There is a need for students to understand and be able to construct
    7·1 answer
  • Sasha drinks 2.5 liters of water each weekday.She drinks a total of 3 liters of water on the weekend.What is the to total volume
    7·1 answer
  • student receives the following​ grades, with an A worth 4​ points, a B worth 3​ points, a C worth 2​ points, and a D worth 1 poi
    9·1 answer
  • 3.8y+4/7x+2=0 for y =?
    10·1 answer
  • Xavier is currently eating 15 chips per minute. At this rate, how many chips will Xavier eat in 7 minutes?
    8·1 answer
  • Which of these problem types can not be solved using the Law of Sines?
    6·2 answers
  • Nora read 1/9 of a book on Monday and 2/5 on Tuesday. What fraction of the book does she have left to read
    8·1 answer
  • The difference of the two numbers is 1.Their sum is 23.find the numbers
    10·1 answer
  • When Mrs. Campece bakes chocolate chip cookies, she need 2 cups of flour
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!