Mike tabulated the following values for heights in inches of seven of his friends: 65, 71, 74, 61, 66, 70, and 72. Mike wishes to construct a 95% confidence interval. What value of t* should Mike use to construct the confidence interval? Answer choices are rounded to the hundredths place.

a) 95% confidence intervals are

(64.188, 72.652)

b) Mike use  

(t₀.₀₂₅ , ₆)= 2.4469

Step-by-step explanation:

Step(i):-

Given data

    x    :     65    71    74    61    66    70   72

Mean of 'x'

     x⁻ = ∑ x / n

 x       :     65          71        74          61        66         70          72

x - x⁻   :    -3.42     2.58     5.58      -7.42      -2.42    1.58        3.58

(x-x⁻)² :      11.69   6.65     31.13     55.05     5.85      2.49      12.81

∑((x-x⁻)²) =  125.67

Variance

             S² = ∑((x-x⁻)²) / n-1 =

Standard deviation S = √20.945 =4.576

Step(ii):-

95% confidence intervals are determined by

Degrees of freedom

ν =n-1 = 7-1 =6

  = (t₀.₀₂₅ , ₆)= 2.4469

( 68.42 - 4.232, 68.42 + 4.232)

(64.188, 72.652)

Conclusion:-

95% confidence intervals are

(64.188, 72.652)