Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = $5
For the alternative hypothesis,
µ < $5
number of samples taken = 10
Sample mean, x = (4 + 3 + 2 + 3 + 1 + 7 + 2 + 1 + 1 + 2)/10 = 2.6
To determine sample standard deviation, s
s = √(summation(x - mean)/n
n = 12
Summation(x - mean) = (4 - 2.6)^2 + (3 - 2.6)^2 + (2 - 2.6)^2 + (3 - 2.6)^2 + (1 - 2.6)^2 + (7 - 2.6)^2 + (2 - 2.6)^2 + (1 - 2.6)^2 + (1 - 2.6)^2 + (2 - 2.6)^2 = 30.4
s = √30.4/10 = 1.74
Since the number of samples is 10 and no population standard deviation is given, the distribution is a student's t.
Since n = 10,
Degrees of freedom, df = n - 1 = 10 - 1 = 9
t = (x - µ)/(s/√n)
Where
x = sample mean = 2.6
µ = population mean = 5
s = samples standard deviation = 1.74
t = (2.6 - 5)/(1.74/√10) = - 4.36
We would determine the p value at alpha = 0.05. using the t test calculator. It becomes
p = 0.000912
