the following data show the number of hours per day 12 adult

the following data show the number of hours per day

12 adults spent in front of screens watching television-related content. Complete parts a and b below.

1.6

4.7

3.7

5.5

7.1

6.5

5.4

2.1

5.3

1.9

2.2

8.2

The 95% confidence interval to estimate the average number of hours per day adults spend in front of screens watching television-related content is from (blank) hours to (blank)hours.

(Round to two decimal places as needed.)

b.

What assumptions need to be made about this population?

A.

The only assumption needed is that the population distribution is approximately uniform.

B.

The only assumption needed is that the population standard deviation is known.

C.

The only assumption needed is that the population distribution is approximately normal.

D.

No assumptions are required.

Solution

a)

Getting the mean and standard deviation,

X = 4.516666667
s = 2.21147147

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    4.5166666          
t(alpha/2) = critical t for the confidence interval =    2.20098516          
s = sample standard deviation =    2.21147147          
n = sample size =    12          
df = n - 1 =    11          
Thus,              
              
Lower bound =    3.111564664          
Upper bound =    5.921768536          
              
Thus, the confidence interval is              
              
(   3.111564664   ,   5.921768536   ) [ANSWER]

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OPTION C: The only assumption needed is that the population distribution is approximately normal.