A random sample of 5 homes in Newberry, Florida had a mean of $169,900 and a standard deviation of $21,756. Construct a 95% confidence interval for the average home of this size in Newberry.
A. (144885.25, 194914.75).
B. (150440.842, 189359.16).
C. (150830, 188969.98).
D. (142886, 196914).

Answers

Answer 1

Answer:

D. (142886, 196914).

Step-by-step explanation:

To solve for this question, we would use t score instead of z score. The reason is because, our sample size is small.

The formula for Confidence Interval =

C.I = Mean ± t score × standard deviation/√n

n = 5 samples

Degrees of freedom = n - 1 = 5 - 1 = 4

The t score for a 95% confidence interval with degrees of freedom 5 is : 2.776

Hence,

Confidence Interval =

169,900 ± 2.776 × 21,756/√5

169,900 ± 2.776 × 9.7295789837

169, 900 ± 27009.311259

Confidence Interval

169,900 - 27009

= 142886

169, 900 + 27009.311259

= 196914

Hence, the confidence interval = (142886, 196914)

Option D is the correct answer

Answer 2

Using the t-distribution, it is found that the 95% confidence interval for the average price of a home of this size in Newberry is of (142886, 196914), given by option D.

In this problem, we have the standard deviation for the sample, thus, the t-distribution is used to solve this question.

The sample mean is [tex]\overline{x} = 169900[/tex].The sample standard deviation is [tex]s = 21756[/tex].The sample size is [tex]n = 5[/tex]

First, we find the number of degrees of freedom, which is the sample size subtracted by 1, so df = 5 - 1 = 4.

Then, we find the critical value for the 95% confidence interval with 4 df, which looking at the t-table or using a calculator is given by t = 2.7765.

The margin of error is:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

In this case:

[tex]M = 2.7765\frac{21756}{\sqrt{5}} = 27014[/tex]

The confidence interval is:

[tex]\overline{x} \pm M[/tex]

Then

[tex]\overline{x} - M = 169900 - 27014 = 142,886[/tex].

[tex]\overline{x} + M = 169900 + 27014 = 196,914[/tex].

Thus, the correct option is D. (142886, 196914).

A similar problem is given at https://brainly.com/question/15180581


Related Questions

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b) Elevator 1 is 16 feet above ground level, and elevator 2 is 25 feet below ground level.

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Answer:

Your answer is B) Elevator 1 is 16 feet above ground level, and elevator 2 is 25 feet below ground level.

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

hope this helps

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Answers

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Answers

Answer:

60 questions in total

Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

100

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

B

Step-by-step explanation:

120/60=2

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Answers

Answer:

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2000: $2.00

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Step-by-step explanation:

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Answers

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Answer:

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Step-by-step explanation:

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Answers

Answer:

(1) 499 and 500 are the greatest consecutive whole numbers whose sum is less than 1000.

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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15/41

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Step-by-step explanation:

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Answers

Answer:

1. 3. 6.

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

3

Step-by-step explanation:

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X y
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Answers

Answer:

27

Step-by-step explanation:

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An artist mixes colors for a painting. She mixes 1.5 ounces of blue with 2.5 ounces of yellow to get the perfect shade of green. If she determines that she will need 12 ounces of green, how much yellow paint will she need?

Answers

Answer:

4.5 ounces of yellow and 7.5 ounces of blue will create 12 ounces of the perfect shade of green.

Step-by-step explanation:

1.5 + 2.5 = 4 ounces.

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Answers

Answer: it should be 68%

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Answers

Answer:

1/4 en pedazos seria 1/4 en pedazos

Step-by-step explanation:

la pregunta no tiene sentido

Answer: La fracción un cuarto, escrita en símbolos como 1/4, significa "una pieza, donde se necesitan cuatro piezas para formar un todo". La fracción un cuarto, escrita en símbolos como 1/4, significa "una pieza, donde se necesitan 4 piezas para formar un todo".

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