Question

STARS	ARR_AUG
5	160
5	173
5	174
5	225
5	195
5	136
5	114
4	159
4	109
4	148
4	132
4	128
4	63
3	130
3	60
3	70
3	65
3	90
2	55
1	90
4	51
4	100
3	120
3	60
3	55
2	60
2	104
2	110
2	50
1	128
4	105
3	104
2	53
2	44
1	54
1	35
2	50
1	49
1	45
1	55
1	55
1	40
3	55
4	97
2	40
5	235
5	132
5	240
5	130
4	152
4	211
4	160
4	102
4	178
4	91
3	104
3	33
5	140
4	75
3	75
3	70
3	90
5	180
4	250
3	84
3	218
3	95
2	40
2	55
1	35
3	70
2	100
1	20
2	41
2	100
1	100
1	120
1	120
1	35
3	100
2	45
1	65
1	50
1	70
1	35
4	265
4	218
2	95
2	150
2	100
5	90
5	211
5	162
5	138
5	128
5	187
5	183
5	150
5	211
5	160
4	56
4	123
4	213
4	124
3	91
4	134
4	120
4	100
3	75
3	90
3	120
3	95
3	120
3	80
3	68
3	100
2	55
2	90
2	120
2	73
2	120
4	180
2	120
2	45
2	70
2	80
1	45
1	50
2	80
3	120
1	31
1	40
1	40
1	23
1	40

George also believes that the mean of the average room rate in August for 4 stars hotels is smaller than the mean of the average room rate in August for 5 stars hotels.
4.1 State the null and the alternative hypotheses.
4.2 Test the null hypothesis at α = 5%. Use a Student-t statistic and unequal variances in the two populations.
4.3 On the basis of your results, do you agree with George? Explain briefly.

Answer 1

Ans) Given data is the mean of the average room rate in August for 4 stars hotels is smaller than the mean of the average room rate in August for s stars hotels. a) state the null and albernative hypothesis. We already know that Null hypothesis ; H.: uiis starts Altanate hypothesis : HA: la lls stars Ho: el 4 stars - Ms stars I HA: llu stars a lls stars - 0 b) student t-statistic & Test the null hypothesis at a=5%. Use a un equal variences in ther a populations, By using spss; we get p-value at d-tailed is 0.029 - But here after that alternative hypothesis (HA) is then divide by (Y2) so the ab 1-tailed P-value is 0.02 Scanned with By using [X=0.05] -0.05 CamScanner → 0.01

out the test statistic &į unequal variences in the two Let us find Populations. Levene's test for of voqiances F I sig b i i sig (a-tailed I ARR _ AUG) Equal variences assumed df 49 2.316 1:34 I 2.174 0.035 2.248 48.011 0.029 Equal voriences not assumed Here we finded test statistic, df, f, sig (one-tailed), sig (2-tailed) cs Scanned with CamScanner

943) We already know P-valve is 0.0f 20.05 so, we are reject the null hypothesis that is statistically significant that the average room rate in August for y stars hotels is smaller than the average room rate in August for s stars hotels. CS Scanned with CamScanner