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UNO [17]
2 years ago
12

A sample of 81 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of th

e program on a scale of 1 to 10, with 10 corresponding to "completely effective" and 1 corresponding to "completely ineffective". The average rating was 5.6 and the standard deviation was 4.6. Construct a 95% confidence interval for the mean score. 5.2 < μ < 6.0 0 < μ < 5.6 4.6 < μ < 6.6 5.1 < μ < 6.1
Mathematics
1 answer:
Kruka [31]2 years ago
4 0

Answer:

95% confidence interval for the true mean score is [4.6 , 6.6].

Step-by-step explanation:

We are given that a sample of 81 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10.

The average rating was 5.6 and the standard deviation was 4.6.

Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;

                      P.Q. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample average rating = 5.6

            s = sample standard deviation = 4.6

            n = sample of tobacco smokers = 81

            \mu = population mean score

<em>Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>

<u>So, 95% confidence interval for the population mean score, </u>\mu<u> is ;</u>

P(-1.993 < t_8_0 < 1.993) = 0.95  {As the critical value of t at 80 degree of

                                            freedom are -1.993 & 1.993 with P = 2.5%}  

P(-1.993 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 1.993) = 0.95

P( -1.993 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 1.993 \times {\frac{s}{\sqrt{n} } } ) = 0.95

P( \bar X-1.993 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+1.993 \times {\frac{s}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-1.993 \times {\frac{s}{\sqrt{n} } } , \bar X+1.993 \times {\frac{s}{\sqrt{n} } } ]

                                            = [ 5.6-1.993 \times {\frac{4.6}{\sqrt{81} } } , 5.6+1.993 \times {\frac{4.6}{\sqrt{81} } } ]

                                            = [4.6 , 6.6]

Therefore, 95% confidence interval for the true mean score is [4.6 , 6.6].

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kodGreya [7K]

Answer:

7.) 16.7

Step-by-step explanation:

7). First you have to find the length of the line with the triangle that is at a 90 angle with the longest side of the triangle

Using the pythagrorem theorem a² + b² = c²

4² + b² = 5²

b² = 5² - 4²

b² = 25 - 16

b² = 9

√b² =√9

b = 3

next you do the same thing to find the missing segment of the longest side

3² + b² = 13²

b² = 169 - 9

b² = 160

b = √160 or  ≈ 12.7

12.7 + 4 = 16.7

so 16.7 is the length of that side


3 0
3 years ago
The area of the surface of a circular pond is needed. A measure about the pond gives a circumference of about 47 feet. Find the
Whitepunk [10]

Answer:

55.95 ft²

Step-by-step explanation:

Circumference formula:  C = 2πr  =>  r = C / (2π)

Area formula:  A = πr²

Substituting C / (2π) for r in the above equation, we get:

               C                        47 ft

A = π( ----------- )²  =  π ( -------------- )²

              2π                       (2π)

or ...

          π(47 ft)²                   2209 ft²

A = ----------------------  =  --------------------  =  55.95 ft²

               4π²                   4(3.14159)²

3 0
2 years ago
Can someone please help me am failing
vichka [17]
All together it equals (of the number of hours he does in a week)
45 because 6 plus 9 is 15 and 15 multipled by 3 is 45 makes sense becuase .. 6 +3 is 9 and 9 +9 is 18 2 weeks equals 14 days 18 subtracted by 14 equals 2 which 45 subtracted by 2 is 43 and that's the esact number of hours he works 43 in a week.
7 0
3 years ago
NEED AWNSERS ASAP!!!​
Naddik [55]

Answer:

3x+2x=95

5x=95

X=19

Step-by-step explanation:

it may help you to understand

5 0
3 years ago
HELP!!
yan [13]

Answer: (15,180) y=0x+180 y=10x+30

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
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