Answer:
Step-by-step explanation: We would set up the hypothesis test. a) For the null hypothesis,
µ ≤ 30
b) For the alternative hypothesis,
µ > 30
It is a right tailed test.
c) the critical value is the t test statistic value
d) Since no population standard deviation is given, the distribution is a student's t.
Since n = 250,
Degrees of freedom, df = n - 1 = 250 - 1 = 249
t = (x - µ)/(s/√n)
Where
x = sample mean = 30.45
µ = population mean = 30
s = samples standard deviation = 5
t = (30.45 - 30)/(5/√250) = 1.42
e) We would determine the p value using the t test calculator. It becomes
p = 0.078
f) Since alpha, 0.1 is > than the p value, 0.078, then we would reject the null hypothesis.
g) the population and the data sampled is normally distributed
f) degree of freedom = 249
