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castortr0y [4]
3 years ago
7

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time student

s spent studying per week. They sampled 240 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours, what is the confidence interval at the 95% level of confidence? (Please use Student's t distribution (Appendix B.5) at infinite degrees of freedom for three decimal accuracy of the required z value.)
Mathematics
1 answer:
Butoxors [25]3 years ago
7 0

Answer: (21.541,\ 23.059)

Step-by-step explanation:

The confidence interval for population mean is given by :-

\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

Given : Sample size : n=240 , which is a large sample , so we apply z-test .

Sample mean : \overline{x}=22.3

Standard deviation : \sigma= 6

Significance level : \alpha=1-0.95=0.05

Critical value : z_{\alpha/2}=1.960

Now, a confidence interval at the 95% level of confidence will be :-

22.3\pm(1.960)\dfrac{6}{\sqrt{240}}\\\\\approx22.3\pm0.759\\\\=(22.3-0.759,\ 22.3+0.759)\\\\=(21.541,\ 23.059)

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8 0
3 years ago
What is the sum of series is numbers 64&amp;66 ?<br> Using the summation notation
iragen [17]

Answer:

64. 6138

66. 8.078125

Step-by-step explanation:

Let's take it one number at a time.

For number 64:

6(2)^{1-1}=6

6(2)^{2-1}=12

6(2)^{3-1}=24

6(2)^{4-1}=48

6(2)^{5-1}=96

6(2)^{6-1}=192

6(2)^{7-1}=384

6(2)^{8-1}=768

6(2)^{9-1}=1536

6(2)^{10-1}=3072

Sum = 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072

Sum = 6138

For number 66:

12(-\frac{1}{2})^{0}=12

12(-\frac{1}{2})^{1}=-6

12(-\frac{1}{2})^{2}=3

12(-\frac{1}{2})^{3}=-1.5

12(-\frac{1}{2})^{4}=0.75

12(-\frac{1}{2})^{5}=-0.375

12(-\frac{1}{2})^{6}=0.1875

12(-\frac{1}{2})^{7}=-0.0078125

12(-\frac{1}{2})^{8}=0.046875

12(-\frac{1}{2})^{9}=-0.0234375

Sum = 12 + -6 + 3 + -1.5 + 0.75 + -0.375 + 0.1875 + -0.0078125 + 0.046875 + -0.0234375

or to make things simpler:

Sum = 12 - 6 + 3 - 1.5 + 0.75 - 0.375 + 0.1875 - 0.0078125 + 0.046875 - 0.0234375

Sum = 8.078125

4 0
3 years ago
Harpreet, Sukhpreet and Komalpreet are three sisters. Sukhpreet is x years old. Harpreet is 3 years older than Sukhpreet. Komalp
Ira Lisetskai [31]

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12

Step-by-step explanation:

Givens

Harpreet        = x + 3

Sukhpreet     = x

Komalpreet   = 2*(x + 3)

Average Age = 15

Equation

[(x + 3) + x + 2*(x + 3) ] / 3 = 15                  Multiply both sides by 3

Solution

3 [(x + 3) + x + 2*(x + 3) ] / 3 = 15 * 3         Combine

 [(x + 3) + x + 2*(x + 3) ]       =   45             Remove the brackets

x + 3 + x + 2x + 6                 =   45             Combine like terms

4x + 9 = 45                                                 Subtract 9 from both sides

4x + 9 - 9 = 45 - 9                                       Combine

4x = 36                                                         Divide by 4

4x/4 = 36/4

x = 9

Answer

Harpreet is  x+ 3 = 9 + 3 = 12

3 0
2 years ago
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s344n2d4d5 [400]

Answer:

It depends, Y or X have to be set up to get an actual number because you can simply plug any numbers.

6 0
3 years ago
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Aneli [31]
Let's use tenths. 

1/10 = 0.10
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<span>1/10 + 5/10 = 6/10 = 0.6</span>
3 0
2 years ago
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