Reference no: EM131641571

Guidelines

- One Word file should be used to submit the full assignment. If you make calculations in Excel and import the tables, be sure that the full table appears on the same page of your document.

- Your file should be named: SE2 Lastname Firstname

- Use the Harvard referencing system throughout the report.

Part 1

Keywords:Confidence Intervals for Means, Normal distribution, t-student distribution

Exercise1. For the following data set

114	112	123	111	109	103
112	113	107	129	108	126
131	129	126	115	123	108
131	115	134	133	132	114
104	127	128	137	114	139
128	117	121	110	141	121
138	140	122	130	115	102

Table 1: Data set Exercise 1

Construct a 1.90% confidence interval for the population mean; 2.95% confidence interval for the population mean; 3.99% confidence interval for the population mean;

4.What assumption do you need to make about the population of interest to construct the confidence intervals ?

Exercise 2. For the following data set

136	141	137	145
131	135	138	136
130	132	136	134
137	133	141	139

Table 2: Data set Exercise 2

Construct a

1.90% confidence interval for the population mean;

2.95% confidence interval for the population mean;

3.99% confidence interval for the population mean;

4.What assumption do you need to make about the population of interest to construct the confidence intervals

Exercise 3. Two boxes, A and B contain equal numbers of balls (black and white). A sample of 100 balls selected with replacement from each of the boxes revealed 52 white balls form box A and 44 white balls from box B.

1. Test the hypothesis that the two boxes have equal ratio of white balls, using a significance level of 0 .05 2.Test the hypothesis that box A has greater ratio of white balls than box B, using a significance level of 0.05

Exercise 4. Consider the sample data for grades A, B, C & D of four different classes, which are tabulated in table 3. Test whether the four means are equal at the 0.05 level of significance.

Perform a test that will compare all 4 means at once. We are not interested in pair-wise comparisons at this stage.

Please show all the steps in your calculations.

Table 3: Data set Exercise 4

80	81	83	78
83	79	72	79
80	83	80	80
65	76	81	98
92	65	87	57
81	74	68	81
65	34	68	71
34	45	78	91
57	61	51	46
71	69	66	72
71	59	63	82
81	67	61	52
72	75	64
81	80	74
36	55	78
83	67
91	94
73
51
98