Question

In: Statistics and Probability

Is there a difference between the means of the total of rooms per hotel in Crete...

Is there a difference between the means of the total of rooms per hotel in Crete and Southern Aegean Islands? Answer your question by calculating an appropriate, symmetric, 95% confidence interval using a Z statistic and equal standard deviations in the two populations. Explain your findings.

REGION ID

1= Crete
2=Southern Aegean Islands
3=Ionian Islands

Total_Rooms Region_ID
412 1
313 1
265 1
204 1
172 1
133 1
127 1
322 1
241 1
172 1
121 1
70 1
65 1
93 1
75 1
69 1
66 1
54 1
68 1
57 1
38 1
27 1
47 1
32 1
27 1
48 1
39 1
35 1
23 1
25 1
10 1
18 1
17 1
29 1
21 1
23 1
15 1
8 1
20 1
11 1
15 1
18 1
23 1
10 1
26 1
306 2
240 2
330 2
139 2
353 2
324 2
276 2
221 2
200 2
117 2
170 2
122 2
57 2
62 2
98 2
75 2
62 2
50 2
27 2
44 2
33 2
25 2
42 2
30 2
44 2
10 2
18 2
18 2
73 2
21 2
22 2
25 2
25 2
31 2
16 2
15 2
12 2
11 2
16 2
22 2
12 2
34 2
37 2
25 2
10 2
270 3
261 3
219 3
280 3
378 3
181 3
166 3
119 3
174 3
124 3
112 3
227 3
161 3
216 3
102 3
96 3
97 3
56 3
72 3
62 3
78 3
74 3
33 3
30 3
39 3
32 3
25 3
41 3
24 3
49 3
43 3
9 3
20 3
32 3
14 3
14 3
13 3
13 3
53 3
11 3
16 3
21 3
21 3
46 3
21 3

Solutions

Expert Solution

Sol:

Descriptive statistics
Region1_Total_Rooms Region2_Total_Rooms
Mean 82.31111111 86.66666667
Variance 9202.219192 10119.77273
Observations 45 45
Pooled Variance 9660.99596

Null hypothesis

Ho:

Ha:

alpha=0.05

Sp=pooled standard deviation

=sqrt((n1-1)*s1^2+(n2-1)*s2^2/(n1+n2-2)

=sqrt(45-1)*9202.219192+(45-1)*10119.77273/(45+45-2))

=98.29037

95% confidence interval for difference in means assuming equal variances is

(x1bar-x2bar)+-Z*Sp*sqrt(1/n1+1/n2)

=(82.3111-86.6667)+-1.96*98.29037*sqrt(1/45+1/45)

=-4.356+-1.96*98.29037*sqrt((1/45+1/45))

=-4.356+-40.614

=-4.356-40.614,-4.356+40.614

=-44.97,36.26

This confidence interval contains 0

Fail to reject Ho

Accept Ho

Conlclusion:

There is no sufficient statistical evidence by 95% confidence interval that

there is a difference between the means of the total of rooms per hotel in Crete and Southern Aegean Islands.

orchestra answered 2 years ago
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