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
12.917 rounded to the nearest ones
adelina 88 [10]
I am pretty sure the answer is 13
6 0
3 years ago
Read 2 more answers
Mr butterworth baked a cake in the shape of a cylinder the cake had a diameter of 9 in and a height of 5 in. He spread chocolate
Luden [163]
So, we need to find {  curved surface area[pi*d*h] + top area[pi*(d^2)/4]  }

just
substitute.
7 0
3 years ago
Read 2 more answers
Kronos Industries bought a desktop for $3,000. It is expected to depreciate at a rate of 10% per year. What will the value of th
kolbaska11 [484]

Answer:

$1968

Step-by-step explanation:

It will depreciate by 10% 4 times, which means that the result in the end will be <em>$3000 * (100% - 10%) * (100% - 10%) * (100% - 10%) * (100% - 10%)</em>, or, put simply, <em>x = $3000 * (0.9)⁴</em>.

Power: x = $3000 * 0.6561

Multiply: x = 1968.3 ≈ $1968

4 0
3 years ago
Which expression gives the solutions -5x+2x^2=-6x?(1pt)
irina [24]
This is the concept of algebra, the solution of the given expression will be given as follows;
-5x+2x²=-6x
adding 5x on both sides we get
5x-5x+2x²=-6x+5x
2x²=-x
divide both sides by 2
(2x²)/2=-x/2
x²=-x/2
divide both sides by x
(x²)/x=-x/(2x)
x=-1/2
the answer is x=-1/2
8 0
3 years ago
A geologist visits 90 volcanoes in Alaska and California​
Viktor [21]

Answer:

40 volcanoes = 100% of them           15% were in California so if we want to know how much % were in Alaska we do 100% - 15% which equals 85%, so 85% were in Alaska.      Now to find out how many the geologist visited in each state multiply 40 by the percentage.       Number of volcanoes in California = 15% of 40 volcanoes = 0.15 x 40 = 6Number of volcanoes in Alaska = 85% of 40 volcanoes 0.85 x 40 = 34

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • If a axbxc=0, and a and b are integers greater than 10, what must c equal
    11·2 answers
  • What is 28 divide by 3
    14·2 answers
  • The sum of 2 times a number and 5 times its reciprocal is 23/3. find the number(s).
    6·1 answer
  • Which of the following is a factor of 3x^3+18x^2+27x? <br> A. 9x<br> B. x^3<br> C. x+3<br> D. x-3
    6·1 answer
  • Least to greatest -20 7/20,7/28,20,20.75
    10·2 answers
  • What does a + a equal to
    14·1 answer
  • PLEASE HELP ME WITH NUMBER 41. find the value of x Pleaseeee
    10·1 answer
  • Integrate with respect to x<br><br> -2/3√((2-5x)^3)
    15·1 answer
  • Is (x + 7) a factor of f(x) = x3 − 3x2 + 2x − 8
    11·1 answer
  • Cheap Car Shop charges $77 for parts and $31 per hour of labor for a repair job. Best Repair in Town charges a flat fee of $150
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!