Mathematics, 07.04.2020 15:40 firstone04kr

You haven't been getting much sleep lately and want to see how you compare to the average CSU student. You plan to sample students and ask them how many hours they sleep per night. Then you will use that data to estimate the population average nightly hours of sleep with an approximate 95% confidence interval. (Critical value 2.) Based on your own sleep, you estimate the standard deviation of hours slept to be 2 hours. What is the minimum number of students you need to sample in order to have a margin of error at most 0.4 hours?

Answers: 2

Show answers

Answers

Answer from: bhopainting

Using the z-distribution, it is found that the minimum sample size is of 97 students.

The first step is finding the critical value, which for a confidence level of $\alpha$ , is given by Z with a p-value of $\frac{1 + \alpha}{2}$ .

In this problem, 95% confidence interval, thus $\alpha = 0.95$ , and Z has a p-value of $\frac{1 + 0.95}{2} = 0.975$ , thus z = 1.96.

The margin of error is:

$M = z\frac{\sigma}{\sqrt{n}}$

In which:

$\sigma$ is the population standard deviation.n is the sample size.

In this problem:

Population standard deviation of 2 hours, thus $\sigma = 2$ Margin of error of 0.4 hours, thus M = 0.4

.The minimum sample size is n, thus:

$M = z\frac{\sigma}{\sqrt{n}}$

$0.4 = 1.96\frac{2}{\sqrt{n}}$

$0.4\sqrt{n} = 3.92$

$\sqrt{n} = \frac{3.92}{0.4}$

$(\sqrt{n})^2 = (\frac{3.92}{0.4})^2$

n = 96.04

Rounding up, the minimum sample size is of 97 students.

A similar problem is given at link

Answer from: teckadeck

Given Information:

confidence level = 95%

standard deviation = σ = 2

Margin of error = 0.4

Required Information:

Number of students = n = ?

Number of students = n ≤ 96 (for z-score = 1.96)

Number of students = n ≤ 100 (for z-score = 2)

Step-by-step explanation:

We know that margin of error is given by

margin of error = z*(σ/√n)

since we want to have a margin of error at most 0.4 hours

margin of error ≤ z*(σ/√n)

√n ≤ z*σ/margin of error

n ≤ (z*σ/Margin of error)²

Where z is the corresponding z-score from the z-table, n is the number of students required and σ is the standard deviation.

For 95% confidence level the exact z-score is 1.96

n ≤ (1.96*2/0.4)²

n ≤ 96.04

n ≤ 96

Therefore, a sample size of less or equal to 96 students is required to ensure a margin of error at most 0.4 hours for 95% confidence interval.

If we use the approximate z-score of 2 as given in the question than the required sample size will be

n ≤ (2*2/0.4)²

n ≤ 100

Therefore, a sample size of less or equal to 100 students is required to ensure a margin of error at most 0.4 hours for 95% confidence interval.

Answer from: Quest

-2/

What is the slope of the line? 1) -5/2 2) -2/5 3) 2/5 4) 5/2

Answer from: Quest

570, the answer is 570, hope it

Another question on Mathematics

Mathematics, 21.06.2019 14:10

1. during first 10 seconds 2. between 10 seconds and 35 seconds 3. during 35 seconds to 40 seconds

Answers: 1

Answer

Mathematics, 21.06.2019 16:30

Astandard american eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. assuming the weights of standard eskimo dogs are normally distributed, what range of weights would 99.7% of the dogs have? approximately 26–34 pounds approximately 24–36 pounds approximately 28–32 pounds approximately 29–31 pounds

Answers: 1

Answer

Mathematics, 21.06.2019 16:30

The length of the largest fish is 967.74 times greater than the length of the smallest fish. select a variable expression that shows the length of the largest fish, if 8 is the length of the smallest fish. a. s + 967.74 b. \[ \frac{967.74}{s} \] c. 967.74 - s d. 967. 74s

Answers: 1

Answer

Mathematics, 21.06.2019 17:30

Astudent survey asked: "how tall are you (in inches)? " here's the data: 67, 72, 73, 60, 65, 86, 72, 69, 74 give the five number summary. a. median: 73, mean: 70.89, iqr: 5, min: 60, max: 74 b. 60, 66, 72, 73.5, 86 c. 60, 67, 72, 73, 74 d. 0, 60, 70, 89, 74, 100

Answers: 3

Answer

You know the right answer?

You haven't been getting much sleep lately and want to see how you compare to the average CSU studen...

Questions

Mathematics, 04.09.2020 14:01

Convert decimals to a fraction...

Mathematics, 04.09.2020 14:01

Find the points of intersection of the graphs of the equations.