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
makvit [3.9K]
3 years ago
11

A simple random sample of 60 households in city 1 is taken. In the sample, there are 45 households that decorate their houses wi

th lights for the holidays. A simple random sample of 50 households is also taken from the neighboring city 2. In the sample, there are 40 households that decorate their houses. What is a 95% confidence interval for the difference in population proportions of households that decorate their houses with lights for the holidays
Mathematics
1 answer:
murzikaleks [220]3 years ago
4 0

Answer:

The calculated value of z = - 0.197  falls in the critical region therefore we reject the null hypothesis and conclude that  at  the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays

Step-by-step explanation:

We formulate the null and alternative hypotheses as

H0: p1= p2 there is no difference in population proportions of households that decorate their houses with lights for the holidays

against Ha : p1≠ p2  (claim)  ( two sided)

The significance level is set at ∝= 0.05

The critical value for two tailed test at alpha=0.05 is ± 1.96

or Z∝= 0.05/2= ± 1.96

The test statistic is

Z = p1-p2/√pq(1/n1 +1/n2)

p1= proportions of households  decorating in city 1  = 45/60=0.75

p2= proportions of households  decorating in city 2 = 40/50= 0.8

p = the common proportion on the assumption that the two proportion are same.

p =   \frac{n_1p_1 +n_2p_2}{n_1+n_2}

Calculating

p =60 (0.75) + 50 (0.8) / 110

p=  45+ 40/110= 85/110 = 0.772

so  q = 1-p= 1- 0.772= 0.227

Putting the values in the test statistic and calculating

z= 0.75- 0.8/ √0.772*0.227( 1/60 + 1/50)

z= -0.05/√ 0.175244 ( 110/300)

z= -0.05/0.25348

z= -0.197

The calculated value of z = - 0.197  falls in the critical region therefore we reject the null hypothesis and conclude that  at  the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays

You might be interested in
A quantity with an initial value of 9100 grows continuously at a rate of 0.85% per hour. What is the value of the quantity after
ycow [4]

Answer:

10,962,54

Step-by-step explanation:

we know that

The equation of a exponential growth is equal to

y=a(1+r)^x

where

a is the initial value  

r is the rate of growth

x is the time in hours

y is the value of the quantity

we have

a=9,100\\r=0.85\%=0.85/100=0.0085

substitute

y=9,100(1+0.0085)^x

y=9,100(1..0085)^x

For x=22 hours

substitute

y=9,100(1..0085)^{22} =10,962,54

4 0
3 years ago
C. If one cubic foot contains about 7.5 gallons, how many gallons of water are in the pool? (3 points) I Water: gallons 3. A rec
Dominik [7]

Answer:

<u>One Rectangular Pan</u>

Step-by-step explanation:

Part C cannot be answered since the dimensions of the pool are not given.  Please check the question.

The cake pans may be compared by calculating the volume of each shape:

Rectangular pan:  Volume = Length x Width x Height

  Volume Rectangle = (13")*(9")*(2") = <u>234 in^3</u>

Round pan:  Volume = \pi r^{2} h

  Volume Round = (3.14)*(4")^2(2") = 100.5 in^3

Two round pans will hold 2*(100.5 in^3) or 201 in^3 of batter

One rectangular pan holds 234 in^3.

Go with the rectangular pan if you want more cake.

4 0
1 year ago
6. The sequence is recursive. Find the value of the next term in the sequence.
Alisiya [41]

Answer: the value is 30

Step-by-step explanation:

you are going up by 5 so 25+5 IS 30

CAN I HAVE BRAINLIEST PLEASE

8 0
3 years ago
There are 16 students in a class with wooden pencils. There are 20 students in a class with mechanical pencils. If a school has
svet-max [94.6K]

Answer:

maybe 100 cheak it please

5 0
3 years ago
Read 2 more answers
What is 7 1/4 minus 3 5/8
gogolik [260]
3.625 is the answer. Enjoy!
3 0
3 years ago
Read 2 more answers
Other questions:
  • 8+(-3) full work thx If u can help
    11·2 answers
  • A circle with center (3,5) intersects the y-axis are(0,1). find the radius of the circle, find the coordinates of the other poin
    13·1 answer
  • Can someone help me with some algebra?
    7·2 answers
  • (76-x+(17+4x)(25+7x)​
    14·2 answers
  • √y =x linear or nonlinear
    9·1 answer
  • How many different arrangements of the letters in the word "ALGEBRA" are there?
    6·2 answers
  • A cone-shaped container has a height of 9 inches and diameter of 2.5 inches. It is filled with a liquid that is worth $2 per cub
    11·2 answers
  • Solve for a.–13. 4a = 33.5
    11·1 answer
  • Help please. Geometry.
    5·2 answers
  • Can someone please help with the Surface Area of this. I need the right answer so that i wont get murdered by my mom and so i ca
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!