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
lesantik [10]
3 years ago
5

A sample of 200 observations from the first population indicated that x1 is 170. A sample of 150 observations from the second po

pulation revealed x2 to be 110. Use the 0.05 significance level to test the hypothesis.
Mathematics
1 answer:
igor_vitrenko [27]3 years ago
5 0

Answer:

a) For this case the value of the significanceis \alpha=0.05 and \alpha/2 =0.025, we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

z_{\alpha/2} =1.96

If the calculated statistic |z_{calc}| >1.96 we can reject the null hypothesis at 5% of significance

b) Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8  

c)z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708    

d) Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

Step-by-step explanation:

Data given and notation    

X_{1}=170 represent the number of people with the characteristic 1

X_{2}=110 represent the number of people with the characteristic 2  

n_{1}=200 sample 1 selected  

n_{2}=150 sample 2 selected  

p_{1}=\frac{170}{200}=0.85 represent the proportion estimated for the sample 1  

p_{2}=\frac{110}{150}=0.733 represent the proportion estimated for the sample 2  

\hat p represent the pooled estimate of p

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  

Concepts and formulas to use    

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

Null hypothesis:p_{1} = p_{2}    

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

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)  

a.State the decision rule.

For this case the value of the significanceis \alpha=0.05 and \alpha/2 =0.025, we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

z_{\alpha/2} =1.96

If the calculated statistic |z_{calc}| >1.96 we can reject the null hypothesis at 5% of significance

b. Compute the pooled proportion.

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8  

c. Compute the value of the test statistic.                                                                                              

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.    

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

z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708    

d. What is your decision regarding the null hypothesis?

Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

You might be interested in
What do u do if u have to remember the milestone test that is coming up??
Olin [163]
.The children initially didn't expect to have fun cleaning the attic, but then they discovered the treasure map.

4 0
3 years ago
Read 2 more answers
Boris has 20 Cd's in his music collection. Given that 20% of the CD's are rock music and 60% of them are pop music. How many CD'
kow [346]
The total amount of CD's are 100% so 100 - (20+60) = 20% -> the percentage of the other types of music. Then multiply 20% by 20 to get 4. So there are 4 CD's that are other types of music
6 0
3 years ago
Read 2 more answers
How much, in total, did Noel spend to cash her three most recent paychecks?
Stolb23 [73]

Based on the amount that Noel cashed in each of her most recent paychecks, the amount she spent in total is $10.99.

<h3>How much did Noel spend?</h3>

The bank directory shows that you are charged 1.99% of the amount being cashed as well as a check processing fee of $1.39.

The amount Noel spent is therefore:

= (1.99% x 100.53) + (1.99% x 119.38) + (1.99% x 122.52) + (1.39 x 3 checks)

= 2.00 + 2.38 + 2.44 + 4.17

= $10.99

Find out more on bank charges at brainly.com/question/26494219.

3 0
2 years ago
Can somebody help me with this. Will Mark brainliest.
Troyanec [42]

Answer:

The answer is 36 I believe

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
The table shows the price for buying bouquets of flowers at a farmers market. What is the unit rate?
Effectus [21]
You just need to divided 3 by 9 and it will be 3 or you can divide 6 by 18 and it will be the same so the unite rate is $3
7 0
3 years ago
Read 2 more answers
Other questions:
  • Easy multiplication question ;)
    11·2 answers
  • Which ordered pair is a solution of the equation? y-3=5(x-2) A.) (2,3) B.) (3,2) C.) Both D.) Neither
    14·1 answer
  • A bag contains hair ribbons for a spirit rally. The bag contains 3 black ribbons and 12 green ribbons. Lila selects a ribbon at
    13·2 answers
  • A cookie recipe calls for 6 cups of flour
    6·2 answers
  • What is the solution to the problem?
    11·1 answer
  • A letter is randomly chosen from the word candlestick.find the probability
    5·2 answers
  • Lloyds account has a balance of $-53.50 if he owes the bank more than $40 his account gets closed which of the following is true
    9·1 answer
  • Explain the step(s) needed to solve 4+ p = 1 and then solve for p
    10·1 answer
  • Pregnancy length (in days) is a normally distributed random variable with a mean of 266 days and a standard deviation of 16 days
    15·1 answer
  • BRAINLIST!!!!!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!