Question

Smaller Ships	Larger Ships
93.2	80.1
84.11	85.67
87.48	83.52
83.06	88.79
91	79.9
72.96	82.81
77.41	80.93
85.78	74.96
80.77	91.72
90	78.2
85.45	82.73
86.53	81.63
80.84	89.23
88.14	77.82
86.6	90.5
83.37	85.14
89.38	83.74
75.57	76.82
76.55	76.63
75.33	81.2
85.61	82.33
90.97	74.93
89.18	78.63
88.05	74.91
93.81	83.08
83.33	74.95
89.84	81.86
81.78	81.36
86.21	87.81
91.4	85.18
72.74	86.88
90.37	74.85
76.99	75.21
79.67	81.72
84.61	82.75
84.8	86.59
85.92	75.24
	86.33
	80.44
	83.87
	81.54
	85.7
	78.81
	79.53

• What is the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers?

• At 95% confidence, what is the margin of error?

• What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships?

  ... to ...

Answer 1

Ans:

	Smaller Ships	Larger Ships
1	93.2	80.1
2	84.11	85.67
3	87.48	83.52
4	83.06	88.79
5	91	79.9
6	72.96	82.81
7	77.41	80.93
8	85.78	74.96
9	80.77	91.72
10	90	78.2
11	85.45	82.73
12	86.53	81.63
13	80.84	89.23
14	88.14	77.82
15	86.6	90.5
16	83.37	85.14
17	89.38	83.74
18	75.57	76.82
19	76.55	76.63
20	75.33	81.2
21	85.61	82.33
22	90.97	74.93
23	89.18	78.63
24	88.05	74.91
25	93.81	83.08
26	83.33	74.95
27	89.84	81.86
28	81.78	81.36
29	86.21	87.81
30	91.4	85.18
31	72.74	86.88
32	90.37	74.85
33	76.99	75.21
34	79.67	81.72
35	84.61	82.75
36	84.8	86.59
37	85.92	75.24
38		86.33
39		80.44
40		83.87
41		81.54
42		85.7
43		78.81
44		79.53
mean	84.56	81.74
std. dev	5.659	4.548

Assume equal population variances.

Point estimate for difference=84.56-81.74=2.82

pooled standard deviation=SQRT(((37-1)*5.659^2+(44-1)*4.548^2)/(37+44-2))=5.0845

standard error=5.0845*SQRT((1/37)+(1/44))=1.134

df=37+44-2=79

critical t value=tinv(0.05,79)=1.990

Margin of error=1.990*1.134=2.26

95% confidence interval for difference in mean ratings

=2.82+/-2.26

=(0.56, 5.08)