Answer:
Step-by-step explanation:
The null hypothesis is
H0 : μ1 ≤ μ2
The alternative hypothesis is
H1 : μ1 > μ2
a) it is a one-tailed and also a right tailed test
b) The decision rule is the basis on which the null hypothesis is rejected or not. If 0.08 > p value, reject H0. If 0.08 < p value, do not reject H0.
c) Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)
z = (x1 - x2)/√σ1²/n1 + σ2²/n2
Where
x1 and x2 represents sample means
σ1 and σ2 represents population standard deviations
n1 and n2 represents number of samples
From the information given,
x1 = 2.67
x2 = 2.59
σ1 = 0.75
σ2 = 0.66
n1 = 65
n2 = 50
z = (2.67 - 2.59)/√0.75²/65 + 0.66²/50
= 0.08/√0.00865 + 0.008712
z = 0.61
From the normal distribution table, the probability value corresponding to the z score is 0.73
d) If 0.08 > 0.73, we would reject H0
e) the p-value is 0.73
