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
belka [17]
2 years ago
5

A state legislator wants to determine whether his voters' performance rating (0 - 100) has changed from last year to this year.

The following table shows the legislator's performance from the same ten randomly selected voters for last year and this year. Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the populations of voters' performance ratings are normally distributed for both this year and last year.
Rating (last year): 87 67 68 75 59 60 50 41 75 72

Rating (this year): 85 52 51 53 50 52 80 44 48 57

Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the rating from last year and x2 be the rating from this year and use the formula d=x2âx1 to calculate the paired differences. Round your answer to one decimal place.

Step 2 of 4: Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.

Step 3 of 4: Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 4 of 4: Construct the 90%90% confidence interval. Round your answers to one decimal place.
Mathematics
1 answer:
ra1l [238]2 years ago
4 0

Answer:

Step 1 of 4

Point estimate for the population mean of the paired differences = -8.2

Step 2 of 4

Sample standard deviation of the paired differences = 16.116244

Step 3 of 4

Margin of Error = ±9.326419

Step 4 of 4

90% Confidence interval = (-17.5, 1.1)

Step-by-step explanation:

The ratings from last year and this year are given in table as

Rating (last year) | x1 | 87 67 68 75 59 60 50 41 75 72

Rating (this year) | x2| 85 52 51 53 50 52 80 44 48 57

Difference | x2 - x1 | -2 -15 -17 -22 -9 -8 30 3 -27 -15

Step 1 of 4

Mean = (Σx)/N = (-82/10) = -8.2 to 1 d.p.

Step 2 of 4

Standard deviation for the sample

= √{[Σ(x - xbar)²]/(N-1)} = 16.116244392951 = 16.116244 to 6 d.p.

Step 3 of 4

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = -8.2

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 10 - 1 = 9.

Significance level for 90% confidence interval

= (100% - 90%)/2 = 5% = 0.05

t (0.05, 9) = 1.83 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 16.116244

n = sample size = 10

σₓ = (16.116244/√10) = 5.0964038367

Margin of Error = (Critical value) × (standard Error of the mean) = 1.83 × 5.0964038367 = 9.3264190212 = 9.326419 to 6 d.p.

Step 4 of 4

90% Confidence Interval = (Sample mean) ± (Margin of Error)

CI = -8.2 ± (9.326419)

90% CI = (-17.5264190212, 1.1264190212)

90% Confidence interval = (-17.5, 1.1)

Hope this Helps!!!

You might be interested in
Harper is knitting a scarf for her cousin's birthday. She plans to knit every night, making the scarf 5 centimeters longer each
MissTica

The equation that shows the relationship between x and y is:

y = 5x

A linear equation is in the form:

y = mx + b

where m is the rate of change and b is the initial value of y, y, x are variables.

Let x represent the number of nights knitting and y represent the length of the scarf.

The equation that shows the relationship between x and y is:

y = 5x

Find out more at: brainly.com/question/13911928

8 0
2 years ago
I need help with the diagram for customary and metric I’m giving 100 points.
sukhopar [10]

Answer:

Customary:

Foot, inch, mile, yard.

Metric:

Centimeter, kilometer, meter.

Both:

Area, height, formula, perimeter.

8 0
2 years ago
Read 2 more answers
You measured the width of your front door to be 3 feet and 2 inches. the chair you are trying to get through the door measured t
Citrus2011 [14]
18 inches or 1 foot and 6 inches
multiply 3 feet by 12 and add two to get the width of the door in inches then subtract 20 inches from it to get the difference
5 0
3 years ago
Read 2 more answers
Item 10 At 1:00 P.M., you have 24 megabytes of a movie. At 1:15 P.M., you have 96 megabytes. What is the download rate in megaby
alex41 [277]

Answer:

4.8 megabytes / minute.

Step-by-step explanation:

At the beginning of recording the download you have 24 megabytes.

15 minutes later, you have 96 megabytes.

In 15 minutes you have downloaded 96 - 24 = 72 megabytes

So the question turns out to be  a proportion of

x megabytes / 1 minute = 72 megabytes / 15 minutes.

x = 72/15

x = 4.8 megabytes / minute

3 0
3 years ago
What is the equation of a parabola that opens left with a vertex of (-1,1)
xeze [42]
I think it is not possible to find a certain equation from just a given points, it must have more given information because there is a lot of parabola pass throw (-1,1).
6 0
2 years ago
Other questions:
  • ms.louis buys popcorn in 20kg bags . her daughter eats 9bags of popcorn per month . how many kg of popcorn does her daughter eat
    10·1 answer
  • The population of a country in 1950 was 6.2 X 107. The population in 2030 is
    7·1 answer
  • Can someone solve this for me please?
    5·1 answer
  • Evaluate the following expression:<br> 30 = 5(8 – 6 + 1) - (2^2 - 3)^3
    12·1 answer
  • Can some one help <br> pleassse
    14·2 answers
  • There are 110 calroies per 177.4 grams of cereal X. find how many calories are in 245.5 grams kf this cereal
    11·1 answer
  • G=qd+hd, solve for d
    7·2 answers
  • PLEASE HELP IDHD &gt;~&lt;
    5·1 answer
  • Given the graph above, which equation could represent the function, given a &gt; 1?
    10·1 answer
  • It is claimed that 79% of all Americans live in cities with population greater than 100,000 people.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!