Question

Two friends, Karen and Jodi, work different shifts for the same ambulance service. They wonder if the different shifts average different numbers of calls. Looking at past records, Karen determines from a random sample of 35 shifts that she had a mean of 5.2 calls per shift. She knows that the population standard deviation for her shift is 1.3 calls. Jodi calculates from a random sample of 34 shifts that her mean was 4.8 calls per shift. She knows that the population standard deviation for her shift is 1.2 calls. Test the claim that there is a difference between the mean numbers of calls for the two shifts at the 0.05 level of significance.

(c) Find the critical value.

Answer 1

To Test :-
H0 :- µ1 = µ2
H1 :- µ1 ≠ µ2

Test Statistic :-


Z = 1.33

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2)
Z(α/2) = Z(0.05 /2) = 1.96
| Z | > Z(α/2) = 1.3286 < 1.96
Result :- Fail to Reject Null Hypothesis

Decision based on P value
Reject null hypothesis if P value < α = 0.05 level of significance
P value = P ( Z < 1.3286 )
P value = 0.184
Since 0.184 > 0.05 ,hence we reject null hypothesis
Result :- We fail to reject null hypothesis

Critical values =   1.96

There is insufficient evidence to support the claim that there is a difference between the mean numbers of calls for the two shifts at the 0.05 level of significance.