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
erastovalidia [21]
3 years ago
5

In 1945. an organization surveyed 1100 adults and asked. "Are you a total abstainer from, or do you on occasion consume, alcohol

ic beverages?" Of the 1100 adults surveyed. 363 indicated that they were total abstainers In a recent survey, the same question was asked of 1100 adults and 341 indicated that they were total abstainers Complete parts (a) and (b) below. The proportions of the adults who took the 1945 survey and the recent survey who were total abstainers are .33 and .31. respectively. (Round to three decimal places as needed) Has the proportion of adults who totally abstain from alcohol changed? Use the <<= 0.10 level of significance First verify the model requirements Select all that apply. The sample size is less than 5% of the population size for each sample The data come from a population that is normally distributed. The samples are independent The samples are dependent n_1p_1 (1 - p_1) greaterthanorequalto 10 and n_2p_2(1 - P_2) greaterthanorequalto 10 The sample size is more than 5% of the population size for each sample. Identify the null and alternative hypotheses for this test. Let p_1 represent the population proportion of 1945 adults who were total abstainers and p_2 represent the population proportion of recent adults who were total abstainers Determine the null and alternative hypotheses. H_0: P_1 = P_2 H_1: p_1 notequalto P_2 Find the test statistic for this hypothesis test. (Round to two decimal places as needed) Determine the P-value for this hypothesis test. (Round to three decimal places as needed) Interpret the P-value If the population proportions are equal. one would expect a sample difference proportion greater than the absolute value of the one observed in about out of 100 repetitions of this experiment. (Round to the nearest integer as needed.)
Mathematics
1 answer:
oee [108]3 years ago
7 0

Answer:

n_1 p_1 =1100*0.31=341 \geq 10

n_1 (1- p_1) =1100*(1-0.31)=759 \geq 10

n_2 p_2 =1100*0.33=363 \geq 10

n_2(1- p_2) =1100*(1-0.33)=737 \geq 10

The data come from a population that is normally distributed.

The samples are independent

z=\frac{0.31-0.33}{\sqrt{0.32(1-0.32)(\frac{1}{1100}+\frac{1}{1100})}}=-0.47  

Since is a two sided test the p value would be:  

p_v =2*P(Z  

If the population proportions are equal one would expect a sample difference proportion greater than the absolute value of the 64 observed in about out of 100 repetitions of this experiment.

Step-by-step explanation:

1) Data given and notation  

X_{1}=341 represent the number of  people indicated that they were total abstainers In a recent survey

X_{2}=363 represent the number of people indicated that they were total abstainers In a 1945 survey,

n_{1}=1100 sample 1

n_{2}=1100 sample2

p_{1}=\frac{341}{1100}=0.31 represent the proportion of people indicated that they were total abstainers In a recent survey

p_{2}=\frac{363}{1100}=0.33 represent the proportion of people indicated that they were total abstainers In a 1945 survey,

z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)  

\alpha=0.05 significance level given

n_1 p_1 =1100*0.31=341 \geq 10

n_1 (1- p_1) =1100*(1-0.31)=759 \geq 10

n_2 p_2 =1100*0.33=363 \geq 10

n_2(1- p_2) =1100*(1-0.33)=737 \geq 10

The data come from a population that is normally distributed.

The samples are independent

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if is there is a difference in the two proportions of interest, the system of hypothesis would be:  

Null hypothesis:p_{1} - p_{2}=0  

Alternative hypothesis:p_{1} - p_{2} \neq 0  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{361+343}1100+1100}=0.32  

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.  

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.31-0.33}{\sqrt{0.32(1-0.32)(\frac{1}{1100}+\frac{1}{1100})}}=-0.469    

Statistical decision

Since is a two sided test the p value would be:  

p_v =2*P(Z  

Comparing the p value with the significance level given \alpha=0.1 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that we have a significant differences between the two proportions.  

If the population proportions are equal one would expect a sample difference proportion greater than the absolute value of the 64 observed in about out of 100 repetitions of this experiment.

You might be interested in
PLEASE I NEED HELP
viktelen [127]

Shaded area = Quarter circle area - Equilateral triangle

s \: a = \pi \times ( {radius})^{2}  -  \frac{1}{2}  \times \: base \times \: height \\

s \: a  = \pi \times  {7}^{2}  -  \frac{1}{2}  \times 7 \times 7 \\

s \: a = 49\pi -  \frac{49}{2}  \\

s \: a = 49 \times 3.14 - 24.5

s \: a = 153.86 \:  - 24.5

shaded \:  \: area = 129.36

There you go...

Have a great day ❤

8 0
3 years ago
Read 2 more answers
Rita made $221 for 17 hours of work.At the same rate, how much would she make for 12
Tatiana [17]
221/17 = 13 bucks per hr

for 12 hrs...
13 * 12 = $ 156 <==
3 0
3 years ago
Read 2 more answers
Distribute to simplify
german
<span>Distribute to simplify

</span>4n (p+6) = 4np+24n\qquad \to  \boxed{4np+24n}<span>
</span>
7 0
3 years ago
*PLZ HELP* This goes for all questions...&gt;...Given the following word problems, write an inequality that models the problem,
Aneli [31]

Answer:

  1. At least 10 hours
  2. No more than 7 feet
  3. At least $7.5
  4. More than 3 players

Step-by-step explanation:

1.

  • 20x + 100 ≥ 300
  • 20x ≥ 200
  • x ≥ 200/20
  • x ≥ 10

At least 10 hours

2.

  • 2(8 + x) ≤ 30
  • 8 + x ≤ 15
  • x ≤ 15 - 8
  • x ≤ 7 feet

No more than 7 feet

3.

  • 8x + 20 ≥ 80
  • 8x ≥ 60
  • x ≥ 60/8
  • x ≥ 7.5

At least $7.5

4.

  • 3(p + 3) > 18
  • p + 3 > 18/3
  • p + 3 > 6
  • p > 6 - 3
  • p > 3

More than 3 players

6 0
3 years ago
Read 2 more answers
What is the value of x in the equation 8x+2=4x
babunello [35]

Answer:

-0.5 is the answer

 

3 0
3 years ago
Other questions:
  • 4x - 2y = -2 6x + 3y = 27
    15·1 answer
  • How do find the rate of change
    13·1 answer
  • The mean for 1,2,3,4
    7·1 answer
  • 1) Shaley plans to use $200 she earned from her
    9·1 answer
  • What is X-2&gt;4 does anybody know?
    8·1 answer
  • techwiz Electronics makes a profit of $35 for each MP3 players sold and $18 for each DVD player sold. Last week, techwiz so the
    15·1 answer
  • Which division problem does the number line best illustrate
    12·1 answer
  • In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment t
    10·2 answers
  • Find all solutions of the equation in the interval [0, 2pi).
    13·1 answer
  • Please solve this!!!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!