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
Scilla [17]
2 years ago
15

Suppose that a random sample of size 10 from the N(µ, 9) distribution resulted in a sample mean of x = 2.7. Give an 85% condiden

ce interval for µ. (b) Suppose that a random sample of size 100 from any distribution with mean µ and variance σ 2 resulted in a sample mean of x = 2.7 and a sample variance of s 2 = 1.1. Give a 90% condidence interval for µ. (c) Suppose that a random sample of size 10 from the N(µ, σ2 ) distribution resulted in a sample mean of x = 2.7 and a sample variance of s 2 = 1.1. Give a 95% condidence interval for µ
Mathematics
1 answer:
stellarik [79]2 years ago
5 0

Answer:

a) CI: 1.3

b) CI: 2.5

c) CI: 2.0

Step-by-step explanation:

a) We have a sample of size n=10 and a sample mean of x=2.7.

The σ² of the population is known and is σ²=9 or σ=3.

For a CI of 85%, the z-value is 1.44.

Then the lower and upper limits of the CI are:

LL=M-z*\frac{\sigma}{\sqrt{n} } =2.7-1.44*\frac{3}{\sqrt{10} }=2.7-1.44*\frac{3}{3.162} =2.7-1.4=1.3\\\\UL=M+z*\frac{\sigma}{\sqrt{n} } =2.7+1.4=4.1

The 85% confidence interval for the mean is defined by the values LL=1.3 and UL=4.1.

CI: 1.3

b) In this case, the variance of the population is unknown.

We have to estimate the variance of the population from the variance of the sample.

Sample data:

n = 100

x(mean) = 2.7

s² = 1.1

The CI is defined as

x-t*\frac{s}{\sqrt{n} }

The value of t depends of the degrees of freedom and the percentage of confidence.

In this case, the degrees of freedom are n-1=100-1=99 and the CI is of 90%.

We look up in a t-table and the t-value for this conditions is 1.6604.

We can now calculate the CI

LL: x-t*\frac{s}{\sqrt{n} }=2.7-1.6604*\frac{\sqrt{1.1} }{\sqrt{100} } =2.7-0.2=2.5\\\\UL: x+t*\frac{s}{\sqrt{n} }=2.7+0.2=2.9

The 90% confidence interval for the mean is defined by the values LL=2.5 and UL=2.9.

CI: 2.5

c) In this case, the variance of the population is unknown.

We have to estimate the variance of the population from the variance of the sample.

Sample data:

n = 10

x(mean) = 2.7

s² = 1.1

The CI is defined as

x-t*\frac{s}{\sqrt{n} }

The value of t depends of the degrees of freedom and the percentage of confidence.

In this case, the degrees of freedom are n-1=10-1=9 and the CI is of 95%.

We look up in a t-table and the t-value for this conditions is 2.2622.

We can now calculate the CI

LL: x-t*\frac{s}{\sqrt{n} }=2.7-2.2622*\frac{\sqrt{1.1} }{\sqrt{10} } =2.7-0.7=2.0\\\\UL: x+t*\frac{s}{\sqrt{n} }=2.7+0.7=3.4

The 95% confidence interval for the mean is defined by the values LL=2.0 and UL=3.4.

CI: 2.0

You might be interested in
Answers need to be fractions, if they are not whole numbers. No decimals
ioda
Slope: -4
Y-intercept : (0, -10)
6 0
1 year ago
A briefcase has a three- digit lock code that doesn't include zero as a digit. What is the probability that the lock code consis
storchak [24]

Answer:

1/21.

Step-by-step explanation:

There are 9 digits and the total number of permutations of 3 from 9 is 9P3

= 9!/6!  = 504.

There are 4 even digits so the number of permutations of 3 from these 4 is 4!  (4-3)!  = 4*3*2 = 24.

So the required probability =  24/504

= 1/21.

5 0
3 years ago
What is 48 divided by 8
mylen [45]

48 ÷ 8 = 6

Hope this helps!

8 0
3 years ago
Read 2 more answers
Please help me solve this !<br> will mark brainliest !<br> (spammers reported)
kherson [118]

Answer:

it is five

Step-by-step explanation:

5v-2=8 then v=x2 because 5x2=10-2=8

so 7v-9=5

7 0
2 years ago
Read 2 more answers
What is the value of x? ​
neonofarm [45]

Answer:

12

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • A car can travel 400 miles on a full tank of petrol. A more efficient car can travel 32% further. How many miles can it travel o
    13·1 answer
  • Yuki bought a dress on sale for $72. The sale price was 60% of the original price. What was the original price of the dress?
    15·1 answer
  • I’ll mark brainlest if you get right
    13·2 answers
  • Each of the digits 7, 5, 8, 9 and 4 is used only one to form a three digit integer and a two digit integer. If the sum of the in
    7·1 answer
  • Step 5: Determine the intersection point: approximately (-9,-2)
    7·2 answers
  • The money in Mrs.Finch's savings account earning 1.45% interest.Which number is below greater than 1.45%
    13·2 answers
  • Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6$.
    14·1 answer
  • Complete the statement. Round to the nearest hundredth if necessary.<br><br> 40 oz = lb
    11·2 answers
  • There are 12 dozen pencils in a gross. how many pencils are in 15 gross
    7·1 answer
  • Given g(x) = (2x - 1), what is the value<br> of g(8)?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!