Answer:
Step-by-step explanation:
Let the subscripts n and d represent day and night shifts respectively.
The null hypothesis is
H0 : μn = μd, μn - μd = 0
The alternative hypothesis is
H1 : μn > μd, μn - μd > 0
A) it is a one-tailed and also a right tailed test because of the greater than symbol in the alternative hypothesis.
B)The decision rule is to reject H0: μd ≥ μn If 0.10 > p value
C) Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)
z = (xn - xd)/√σn²/nn + σd²/nd
Where
xn and xd represents sample means for night and day respectively.
σn and σd represents population standard deviations for night and day respectively.
nn and nd represents number of samples
From the information given,
xn = 341
xd = 336
σn = 25
σd = 19
nn = 61
nd = 56
z = (341 - 336)/√25²/61 + 19²/56
z = 1.22
Test statistic = 1.22
D) From the normal distribution table, the probability value corresponding to the area above the z score is 1 - 0.8888 = 0.1112
Since the level of significance, 0.02 < 0.1112, do not reject H0.
