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
UNO [17]
3 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]3 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].

You might be interested in
The curved part of this figures is a semicircle.
Varvara68 [4.7K]
The correct answer for this question is this one:

As shown in the graph, The curved part of this figures is a semicircle.
What is the area of this figure?

28+8.125π units²
<u>28+16.25π units²</u>
14+8.125π units²
14+16.25π units²
Hope this helps answer your question and have a nice day ahead.
6 0
3 years ago
Can anyone do this for me? ty &lt;3
Marta_Voda [28]
Can’t read it but you would subtract The biggest number by the smallest number
6 0
3 years ago
Read 2 more answers
A plumber charges an initial amount,x, to make a house call plus an hourly rate,y, for the time he is working.A 1-hour job costs
Inessa05 [86]
X=$30
y=$60

1 hour job- 60x1=60+30=90
3 hour job-60x3=180+30=210
5 0
3 years ago
Which function is linear?
Mariulka [41]

Answer:

c

Step-by-step explanation:

7 0
3 years ago
There are three different recipes. Two taste the same.
Sauron [17]

Answer:

Mixture 1 and 2

Step-by-step explanation:

4/6 = 2/3

6/9= 2/3

9/12 = 3/4 NOT THE SAME

5 0
3 years ago
Other questions:
  • An ice cream shop uses the following ingredients to make 1 sundae.
    14·1 answer
  • If g(x) =4x^2-16 were shifted 9 units to the right and 1 down, what would be the new equation
    15·2 answers
  • Choose the expression that represents the fraction one thirteenth.
    5·1 answer
  • Write the equation of the line that passes through (3,-2) and is
    8·1 answer
  • Todd takes out a student loan for $25,000. The annual simple interest rate is 7.75%. If Todd will be paying $38,750 in interest
    6·1 answer
  • If the P-value is 0.02, it means that the probability of obtaining the sample statistic is 2%, if the null hypothesis is true. t
    6·1 answer
  • Help plzzzzzzzzzzzzz​
    15·2 answers
  • What is 4.5(x - 9)= -13.5
    12·1 answer
  • Find the circumference of the circle. area = 121pi ft2
    13·1 answer
  • Write the proportion. do not include units in the answer.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!