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
fiasKO [112]
2 years ago
8

Many individuals over the age of 40 develop intolerance for milk and milk-based products. A dairy has developed a line of lactos

e-free products that are more tolerable to such individuals. To assess the potential market for these products, the dairy commissioned a market research study of individuals over 40 years old in its sales area. A random sample of 250 individuals showed that 86 of them suffer from milk intolerance. Based on the sample results, calculate a 90% confidence interval for the population proportion that suffers milk intolerance. Interpret this confidence interval. a) First, show that it is okay to use the 1-proportion z-interval. b) Calculate by hand a 90% confidence interval. c) Provide an interpretation of your confidence interval. d) If the level of confidence was 95% instead of 90%, would the resulting interval be narrower or wider
Mathematics
1 answer:
Alexus [3.1K]2 years ago
6 0

Answer:

a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.

b) See step by step explanation

CI 90 %  =  (  0,296 ; 0,392)

c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392)

d) the CI 95 % will be wider

Step-by-step explanation:

Sample Information:

Sample size n  =  250

number of people with milk intolerance  x = 86

p₁  =  86 / 250    p₁ = 0.344    and   q₁ =  1  - p₁   q₁ = 0,656

To calculate 90 % of Confidence Interval   α = 10%  α/2 = 5 %  

α/2 = 0,05     z(c) from z-table is:  z(c) =  1.6

Then:

CI 90 %  =  (  p₁  ±  z(c) * SE )

SE =  √ (p₁*q₁)/n   =  √ 0,225664/250

SE = 0,03

CI 90 %  =  (  0,344  ±  1,6* 0,03 )

CI 90 %  =  (  0,344 - 0,048 ;  0,344 + 0,048)

b) CI 90 %  =  (  0,296 ; 0,392)

a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.

c) We can support that with 90 % of confidence we will find the random variable between  this interval (  0,296 ; 0,392) .

d) CI 95 %      then significance level α = 5 %   α/2 = 2.5 %  

α/2  =  0,025      z(c) = 1.96   from z-table

SE = 0,03

And  as 1.96 > 1.6    the CI 95 % will be wider

CI 95% =  ( 0,344 ±  1.96*0,03 )

CI 95% =  (  0,344 ± 0,0588 )

CI 95% =  ( 0,2852 ; 0,4028 )

You might be interested in
1 Bradley is building a table
Harman [31]

Answer:

Step-by-step explanation: < 180

3 0
3 years ago
Jillian is trying out for the cross country team. To make the team, she must run 3 1/2 miles in less than 40 mins. Will Jillian
aliina [53]

Answer:

Yes, Jillian will make it for the team, beacuse it's very easy to run 3.5 miles in 40 minutes. Actually, you can run 5 miles very easily in 40 minutes.

My gratitude attitude-THANKS!

5 0
2 years ago
What are the coordinates for the points of intersection
stira [4]

Answer:

d

Step-by-step explanation:

knnjjnjkknnmnm

7 0
2 years ago
Which expression is equivalent to 4 (x + 2)?<br> 6 x<br> 4 (x) + 4 (2)<br> 4 (x) + 4<br> 8x
Andrei [34K]
The answer is b - 4(x) + 4(2)
8 0
3 years ago
Read 2 more answers
Will give brainliest.
Dennis_Churaev [7]
Pretty sure it's A. (X times .5 equals Y)
8 0
2 years ago
Other questions:
  • Please help! I really need help!
    8·1 answer
  • Joe’s rectangular garden is 6 meters long and 4 meters wide. He wishes to double the are of his garden by increasing its length
    12·1 answer
  • The number of bacteria in a sample after x days is represented using the equation b= 50,000(1.05)^-x. By what approximate percen
    10·2 answers
  • Evaluate: −4 + 12 ÷(−3)/10 + 3(−2)
    14·2 answers
  • if there are 300 calories in 100 g of a certain food, how many calories are there in a 30 g portion of food​
    9·1 answer
  • Does anybody like the band: Why don´t we?
    8·1 answer
  • A chemist mixes a 25 % acid solution with a 45% acid solution to make 600 ml of a 30% acid solution. How much of each type of so
    15·1 answer
  • Samantha's parents are going to paint her room. Her color choices for the
    15·1 answer
  • Ants can hear each other up to a range of 2 m. An ant at A, 1 m
    10·1 answer
  • What is the volume of this figure?<br><br> Enter your answer in the box.<br><br> yd³
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!