Question

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.

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

Answer 1

Solution:

4.1 State the null and the alternative hypotheses.

Answer: The null and the alternative hypotheses are:

4.2 Test the null hypothesis at α = 5%. Use a Student-t statistic and unequal variances in the two populations.

Under the null hypothesis, the test statistic is:

Where:

  

Now to find the p-value, we have to find the degrees of freedom. The formula for finding the degrees of freedom is:

Therefore, the p-value is:

4.3 On the basis of your results, do you agree with George? Explain briefly.

Answer: Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and conclude that there is sufficient evidence to agree with George.