q1

An education researcher wanted to examine whether there was a difference in academic performance between students who did face-to-face lessons and those who did online lessons. To achieve this, he recorded the overall scores (upon 100%) of a class of 45 SUSS students who studied Statistics through face-to-face mode during the 2019 July semester. Similarly, he took the overall scores of another class of 50 students who studied Statistics through the online mode during the 2020 July semester.

2019 Jul	2020 Jul
30	35
25	23
33	56
29	60
55	66
62	77
85	85
68	64
80	65
15	88
65	74
40	22
50	36
32	50
40	64
50	55
59	81
90	66
16	49
90	68
40	56
19	63
45	32
49	41
45	53
75	23
80	46
74	77
75	55
90	33
30	78
36	65
50	84
49	32
62	13
80	63
75	33
65	44
66	55
78	77
45	65
34	10
70	70
60	46
46	20
	50
	66
	70
	65
	79

Describe three (3) measures of location and three (3) measures of dispersion. State the values of these measures for both classes. You are required to present the relevant Excel reports.

Q2

A Psychology student wanted to study whether there is a difference in stress levels between gender. She devised a survey to measure stress. There were 20 questions with a total score of 100. She randomly selected 30 male and 30 female students from SUSS to complete the survey

Male	Female
67	70
68	76
67	69
69	75
70	73
68	88
69	68
70	69
70	75
70	79
71	71
71	68
70	71
71	68
72	78
70	76
69	75
69	69
71	69
69	71
70	68
70	76
70	74
72	71
71	69
70	70
71	74
69	80
72	69
71	79

(i) Describe the 90% confidence intervals for the mean stress score of each gender. Based on the confidence intervals, discuss whether we can conclude that the stress level of both genders are similar. You are required to present the relevant Excel reports.

(ii) Apply an appropriate hypothesis test at the 10% significant level to determine whether the stress levels of both genders are similar. You are required to present the relevant Excel report.

(b) A study showed that the length of human pregnancies is normally distributed with mean 266 days and standard deviation 16 days.

i)If twenty (20) women are randomly selected, report the probability that the mean length of pregnancies is greater than 265 days.