Question

find a 95% confidence interval for the mean electricity 
consumption for all days having average temperature 73.6 degrees.  Also, 
find a 95% prediction interval for the electricity consumption for a new 
day with average temperature 73.6 degrees.

temperatureavg  kilowattsperhour

77.5 45
80 73
78 43
78.5 61
77.5 52
83 56
83.5 70
81.5 70
75.5 53
69.5 51
70 39
73.5 55
77.5 55
79 57
80 68
79 73
76 57
76 51
75.5 55
79.5 56
78.5 72
82 73
71.5 69
70 38
68 50
66.5 37
69 43
70.5 42
63 25
64 31
64.5 31
65 32
66.5 35
67 32
66.5 34
67.5 35
75 41
75.5 51
71.5 34
63 19 
60 19
64 30
62.5 23 
63.5 35
73.5 29
68 55
77.5 56

Answer 1

Confidence interval mean electricity consumption is given by

where t_n-1, is the quantile value of t distribution of n-1 df and alpha level of confidence  

we can calculate the quantile value form R

Screenshot is given by

is the sample mean

and n is the sample size

A)

So 95% confidence interval for mean electricity consumption is given by:

then by using above formula  it is given by

(59.37658, 85.49576)

B)

Similarly we can find it for  kilowatts per hour