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
andrey2020 [161]
3 years ago
11

A random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams1 shows that B was the most commo

n correct choice, with 90 of the 400 questions having B as the answer. Does this provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely? Show all details of the test. The data are available in APMultipleChoice.
a) State the null and alternative hypotheses

b) Calculate the test statistic and p-value
Mathematics
1 answer:
maks197457 [2]3 years ago
8 0

Answer:

a) Null hypothesis:p\leq 0.2  

Alternative hypothesis:p > 0.2  

b) z=\frac{0.225 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=1.25  

p_v =P(Z>1.25)=0.106  

Step-by-step explanation:

1) Data given and notation

n=400 represent the random sample taken

X=90 represent the number of questions with B as the correct answer

\hat p=\frac{90}{400}=0.225 estimated proportion of arrests that were not prosecuted

p_o=0.2 is the value that we want to test, since we assume that each question present 5 options and just one is correct, 1/5 =0.2 if all five options were equally likely

\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 is higher than 0.2.:  

Null hypothesis:p\leq 0.2  

Alternative hypothesis:p > 0.2  

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{0.225 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=1.25  

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 provided \alpha. 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>1.25)=0.106  

If we compare the p value obtained and the significance level assumed \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of B correct answers is not significantly higher than 0.2.  

You might be interested in
Answer Please---Due today!!!
Angelina_Jolie [31]

Answer:

14/44 or 7/22

because 44 is the total and the total number of latin cds are 14

so 14/44 simplified would be 7/22

hope it helped

Step-by-step explanation:

Please rate and mark as brainliest

Thank you and have a good day

5 0
1 year ago
Read 2 more answers
A. 3.9<br><br> B. 1.0<br><br> C. 1.7<br><br> D 3.3
amm1812

Answer:

its for sure C

Step-by-step explanation:

4 0
3 years ago
What is the best way to convert metric units (I'm really bad at this...)
Vladimir [108]
Necesitas reconocer los múltiplos u submúltiplos del sistema métrico decimal si son lineales por cada nivel que avanzas multiplicas o divides con el 10
siempre y cuando la unidad de medida es el metro ese queda al centro.
Km Hm Dam m dm cm mm yo los ubico en escalera el metro queda al centro y de cualquier lugar que te posicionas,buscas a donde quieres convertir y revisas si vas a la derecha multiplicas por 10 o si vas a la izquierda divides entre 10 siempre y cuando sea un lugar a donde te vas a mover si son dos lugares es con el 100 por que 10x10 es 100 y si son tres lugares es con el 1000 porque es 10x10x10.
ejemplo 2000m convertirlos a Hm= 20 Hm dividí 2000 entre 100 porque me moví 2 lugares a la izquierda  otro ejem. 100 Dam convertirlos a cm=100000 porque 100x 1000 por que avance 3 lugares a la derecha
4 0
3 years ago
Please help me with this!
Airida [17]

Step-by-step explanation:

→ 42 = 7u - u

→ 42 = 6u

→ 42/6 = u

→ 7 =u or U = 7

<em><u>hope </u></em><em><u>this</u></em><em><u> answer</u></em><em><u> helps</u></em><em><u> you</u></em><em><u> dear</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>take </u></em><em><u>care </u></em><em><u>and</u></em><em><u> may</u></em><em><u> u</u></em><em><u> have</u></em><em><u> a</u></em><em><u> great</u></em><em><u> day</u></em><em><u> ahead</u></em><em><u>!</u></em>

4 0
3 years ago
5c + 9c <br><br>Show your solution! tyms​
S_A_V [24]
5c plus 9c is 14c bc 5 plus 9 is 14 and the exponent is c so 14c
8 0
3 years ago
Read 2 more answers
Other questions:
  • identify the maximum and minimum values of the function y = 3 cos x in the interval [-2π, 2π]. Use your understanding of transfo
    5·1 answer
  • In the top row of an chessboard, Tom writes the values 1, 2, 4, 8, 16, 32, 64, 128. In the leftmost column, Tom writes the value
    12·1 answer
  • (3x^3)( 1/9x^2 - 6 + 2x)
    15·1 answer
  • Solving Equations. 2(a-3)=5a+3a
    8·2 answers
  • ?-66= 25 what is the ?
    12·1 answer
  • A simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard d
    13·2 answers
  • Given the congruent figures solve for the missing variable
    13·1 answer
  • Two sons shared ₦14,000 in the ratio of 4 ratio 3 what are their respective shares<br>​
    6·1 answer
  • Can someone check my answers if they are correct or incorrect? If it is incorrect, please let me know why it is incorrect please
    11·1 answer
  • A certain book has 200 pages, and 47 of these pages have an illustration. If one of the book's pages
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!