To tackle this issue, we need to utilize the t statistic. This requires calculating the t score first and then consulting standard distribution tables to find the corresponding p value based on the obtained t score.
The formula for calculating the t score is:
t = (x – μ) / (σ / sqrt(n))
Where,
x = sample mean = 40
n = number of sample subjects = 16
s = standard deviation = 20
μ = Population Mean = 30
Plugging in the known values:
t = (40 – 30) / (20 / sqrt 16)
t = 10 / 5
t = 2
Utilizing the standard distribution tables and calculating the degrees of freedom, which is n – 1 = 15, we then find:
p = 0.032
Regarding the logarithmic equation, option c is correct: x=6 is a valid solution, while x=-6 is considered an extraneous solution. Explanation: The equation requires dividing both sides by 2, simplifying further until each step can be logically followed based on logarithmic definitions, from which we affirm that both sides equal when substituting back the values, confirming that x=6 is the true solution.
