Answer:
Step-by-step explanation:
Mean = (29.7 + 29.4 + 31.7 + 29.0 + 29.1 + 30.5 + 29.1 + 29.8)/8 = 29.7875
Mean = 29.7875 × 1000 = $29787.5
Standard deviation = √(summation(x - mean)²/n
n = 8
Summation(x - mean)² = (29.7 - 29.7875)^2 + (29.4 - 29.7875)^2 + (31.7 - 29.7875)^2 + (29.0 - 29.7875)^2 + (29.1 - 29.7875)^2 + (30.5 - 29.7875)^2 + (29.1 - 29.7875)^2 + (29.8 - 29.7875)^2 = 5.88875
Standard deviation = √(5.88875/8
s = 0.88
s = 0.88 × 1000 = $880
a) 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,
H0:µ ≤ 30000
For the alternative hypothesis,
H1:µ > 30000
This is a right tailed test.
b) The decision rule is to reject the null hypothesis if the significance level of 0.05 is greater than the probability value. If it is otherwise, we would fail to reject the null hypothesis.
c) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 8
Degrees of freedom, df = n - 1 = 8 - 1 = 7
t = (x - µ)/(s/√n)
Where
x = sample mean = 29787.5
µ = population mean = 30000
s = samples standard deviation = 880
t = (29787.5 - 30000)/(880/√8) = - 0.68
We would determine the p value using the t test calculator. It becomes
p = 0.26
d) Since alpha, 0.1 < the p value, 0.26, then we would fail to reject the null hypothesis.
