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
kirza4 [7]
2 years ago
10

(CO 4) In a sample of 8 high school students, they spent an average of 24.8 hours each week doing sports with a sample standard

deviation of 3.2 hours. Find the 95% confidence interval, assuming the times are normally distributed.
(21.60, 28.00)

(22.12, 27.48)

(22.66, 26.94)

(24.10, 25.50)
Mathematics
1 answer:
AveGali [126]2 years ago
6 0

Answer:  

(22.12, 27.48)

Step-by-step explanation:

Given : Significance level : \alpha: 1-0.95=0.05

Sample size : n= 8 , which is a small sample (n<30), so we use t-test.

Critical values using t-distribution: t_{n-1,\alpha/2}=t_{7,0.025}=2.365

Sample mean : \overline{x}=24.8\text{ hours}

Standard deviation : \sigma=3.2\text{ hours}

The confidence interval for population means is given by :-

\overline{x}\pm t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}

i.e. 24.8\pm(2.365)\dfrac{3.2}{\sqrt{8}}

24.8\pm2.67569206001\\\\\approx24.8\pm2.68\\\\=(24.8-2.68, 24.8+2.68)=(22.12, 27.48)

Hence, the 95% confidence interval, assuming the times are normally distributed.=  (22.12, 27.48)

You might be interested in
Construct equation
ElenaW [278]

Step-by-step explanation:

(x × 5) +6=41

5x + 6=41

5x =41-6

5x=35

x=(35/5)

x=7

6 0
2 years ago
Q1. Find the measure of angle 1. Show your work.
OlgaM077 [116]

Answer:

1. 110°

2. 139°

Step-by-step explanation:

1. 180° in a triangle

180 - 40 - 30 = 110°

2. 180° in a triangle

angles on a straight line add up to 180°

180 - 64 - 75 = 41°

180 - 41 = 139°

4 0
2 years ago
A tropical storm is classified as a hurricane when there are maximum sustained winds of
konstantin123 [22]

Answer: A hurricane usually takes days to develop. The fastest a hurricane might form is in 48 hours or two days. If a cluster of thunderstorms already exists then it might only take a day.

Step-by-step explanation:

8 0
3 years ago
A class of 40 students took a test 20 students had an average score of 65. the other students had an average score of 52. what i
Korolek [52]

Answer:

One: 58.5

Two 36.6

Step-by-step explanation:

One

20 students * 65 = 1300 This is the total score of all 20 students. They may not all get 65, but 1300 is what their average total is.

20 students * 52 = 1040

The total score of all 40 students was 1300 + 1040 = 2340

The average for the entire class was 2340 / 40 = 58.5

Two

This question is done almost the same way.

Supposes the total number of members is 100. That means that 28 of them are men

28 * 33 = 924     This is the total age for the men

100 - 28 = 72        Out of 100, 72 of the people there are women.

72 * 38 = 2736

The total number of years of all of the members is

924 + 2736 = 3660      

The average age of all members is 3660/100 = 36.6

Why did I pick 100 as the total membership? It is because a percentage is number out of 100. Am I allowed to invent things like that? Sure. I'm just using the definition of a percentage.

The average will make it come out the same.

7 0
2 years ago
Arrange the following numbers in increasing order: \begin{align*} A &amp;= \frac{2^{1/2}}{4^{1/6}}\\ B &amp;= \sqrt[12]{128}\vph
prisoha [69]

Answer:

The order is "D, B, A, E, C".

Step-by-step explanation:

The numbers are as follows:

A=\frac{2^{1/2}}{4^{1/6}}\\\\B = \sqrt[12]{128}\\\\C=(\frac{1}{8^{1/5}})^{2}\\\\D = \sqrt{\frac{4^{-1}}{2^{-1}\cdot 8^{-1}}}\\\\E = \sqrt[3]{2^{1/2}}\cdot 4^{-1/4}

Simplify the value of A, B, C, D and E as follows:

A=\frac{2^{1/2}}{4^{1/6}}=\frac{2^{1/2}}{2^{2/6}}=\frac{2^{1/2}}{2^{1/3}}=2^{1/2-1/3}=2^{1/6}=1.1225\\\\B = \sqrt[12]{128}=(128)^{1/12}=(2^{7})^{1/12}=2^{7/12}=1.4983\\\\C=(\frac{1}{8^{1/5}})^{2}=(\frac{1}{(2^{3})^{1/5}})^{2}=(\frac{1}{2^{3/5}})^{2}=\frac{1}{2^{3/5\times2}}=\frac{1}{2^{6/5}}=2^{-6/5}=0.4353\\\\D = \sqrt{\frac{4^{-1}}{2^{-1}\cdot 8^{-1}}}=\sqrt{\frac{2^{-2}}{2^{-1}\cdot 2^{-3}}}=\sqrt{2^{-2+1+3}}=2\\\\E = \sqrt[3]{2^{1/2}}\cdot 4^{-1/4}= (2^{1/2})^{1/3}\cdot 2^{-2/4}=2^{-1/3}=0.7937

Arrange the following numbers in increasing order as follows:

D > B > A > E > C

Thus, the order is "D, B, A, E, C".

7 0
2 years ago
Other questions:
  • Round 406542 to ten thousand
    9·2 answers
  • 1. Write an equation of the circle whose diameter AB has endpoints A(-4,2) and B(4,-4)
    15·1 answer
  • The radius of a circle is 7 centimeters
    10·1 answer
  • The best player on a basketball team makes 80​% of all free throws. The​ second-best player makes 75​% of all free throws. The​
    11·1 answer
  • What is y _ times x?
    5·2 answers
  • NEED HELP PLEASE!!!<br><br> Given f(x)=9x+4 and g(x)= -5x+1, what is g(x)-f(x)?
    8·1 answer
  • Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence,where n = 1 for the
    14·1 answer
  • Given a linear function y =23x+2, which two points make the line?
    7·1 answer
  • PLZ HELP ME ASAP W THIS !!!
    11·1 answer
  • Jocelyn sells necklaces for $8 each. It costs her $20 for
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!