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
labwork [276]
3 years ago
13

Suppose twenty-two communities have an average of = 123.6 reported cases of larceny per year. assume that σ is known to be 36.8

cases per year. find a 90%, 95%, and 98% confidence interval for the population mean annual number of reported larceny cases in such communities. compare the lengths of the confidence intervals. as the confidence levels increase, do the confidence intervals increase in length?
Mathematics
1 answer:
Delvig [45]3 years ago
3 0
We are given the following data:

Average = m = 123.6
Population standard deviation = σ= psd = 36.8
Sample Size = n = 22

We are to find the confidence intervals for 90%, 95% and 98% confidence level.

Since the population standard deviation is known, and sample size is not too small, we can use standard normal distribution to find the confidence intervals.

Part 1) 90% Confidence Interval
z value for 90% confidence interval = 1.645

Lower end of confidence interval = m-z *\frac{psd}{ \sqrt{n} }
Using the values, we get:
Lower end of confidence interval=123.6-1.645* \frac{36.8}{ \sqrt{22}}=110.69

Upper end of confidence interval = m+z *\frac{psd}{ \sqrt{n} }
Using the values, we get:
Upper end of confidence interval=123.6+1.645* \frac{36.8}{ \sqrt{22}}=136.51

Thus the 90% confidence interval will be (110.69, 136.51)

Part 2) 95% Confidence Interval
z value for 95% confidence interval = 1.96

Lower end of confidence interval = m-z *\frac{psd}{ \sqrt{n} }
Using the values, we get:
Lower end of confidence interval=123.6-1.96* \frac{36.8}{ \sqrt{22}}=108.22

Upper end of confidence interval = m+z *\frac{psd}{ \sqrt{n} }
Using the values, we get:
Upper end of confidence interval=123.6+1.96* \frac{36.8}{ \sqrt{22}}=138.98

Thus the 95% confidence interval will be (108.22, 138.98)

Part 3) 98% Confidence Interval
z value for 98% confidence interval = 2.327

Lower end of confidence interval = m-z *\frac{psd}{ \sqrt{n} }
Using the values, we get:
Lower end of confidence interval=123.6-2.327* \frac{36.8}{ \sqrt{22}}=105.34
Upper end of confidence interval = m+z *\frac{psd}{ \sqrt{n} }
Using the values, we get:
Upper end of confidence interval=123.6+2.327* \frac{36.8}{ \sqrt{22}}=141.86

Thus the 98% confidence interval will be (105.34, 141.86)


Part 4) Comparison of Confidence Intervals
The 90% confidence interval is: (110.69, 136.51)
The 95% confidence interval is: (108.22, 138.98)
The 98% confidence interval is: (105.34, 141.86)

As the level of confidence is increasing, the width of confidence interval is also increasing. So we can conclude that increasing the confidence level increases the width of confidence intervals.
You might be interested in
If 3×1=34 2×3=65 6×1=67 5×4=209 then 6×3=
OLga [1]
189.

3*1=34 --> split this into two parts. 3*1 is 3 and 3+1 is 4 so put them together and you get 34.
3 0
3 years ago
Read 2 more answers
Consider h(x)=x^2+8+15. identify its vertex and y-intercept.
OleMash [197]

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, [x = \frac{-b}{2a}, h(\frac{-b}{2a})].

<h3>Use the equation:  [x = \frac{-b}{2a}, h(\frac{-b}{2a})]</h3>

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for <em>a</em> and <em>b</em> into the equation to solve for the x-coordinate of the vertex.

x = \frac{-b}{2a}

x = \frac{-8}{2(1)}

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the <u>y-coordinate of the vertex</u>:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

<h3>Solve for the Y-intercept:</h3>

The <u>y-intercept</u> is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

5 0
2 years ago
Say what now?! I don’t get this please help!
Nuetrik [128]

Answer:

D)

Step-by-step explanation:

7x + 4 = 3x + 68

7x - 3x = 68 - 4

4x = 64

x = 64/4

x = 16

I Hope I've helped you.

7 0
3 years ago
Read 2 more answers
The manager of the customer service division of a major consumer electronics company is interested in determining whether the cu
PolarNik [594]

The best sampling strategy would be a stratified sample.

<h3>How are samples classified?</h3>

Samples may be classified as:

  • Convenient: Drawn from a conveniently available pool.
  • Random: All the options into a hat and drawn some of them.
  • Systematic: Every kth element is taken.
  • Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
  • Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.

For this problem, the 4 different brands of the recorders must be considered, hence the buyers should be divided into groups, and a proportion of each group should be sampled, hence a stratified sample should be used.

More can be learned about sampling at brainly.com/question/25122507

#SPJ1

3 0
2 years ago
Please help <br> -2/5 + 4/5
Savatey [412]

your answer will be 2/5 and if they want to know decimal form it is 0.4

Hope I helped :)

6 0
3 years ago
Other questions:
  • if it cost $75,000 to put on an event and total revenue is $135,000, how much profit did the concert bring in ?
    6·2 answers
  • What is the slope (grade) of a road that rises 6 feet for every horizontal change of 100 feet ?
    15·1 answer
  • Cassidy places 49 stamps on each of 8 albums pages how many stamps does she place?
    14·2 answers
  • 9 is 3% of what number
    7·2 answers
  • Which expressions are equivalent to z0.2?
    10·1 answer
  • The line plot shows the amount of grass seed that a landscaper needs for each of her jobs. What is the total amount of grass see
    6·1 answer
  • !
    12·1 answer
  • What is the common denominator of 1/9 and 5/12
    5·1 answer
  • Darrin surveyed a random sample of 10 students from his science class about their favorite types of TV shows. Five students like
    7·1 answer
  • 14
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!