Question 4: [6 marks]

From an Intro Stats unit, a random sample of 12 students is selected, and their marks from online Lab 5 and online Lab 6 are recorded as "Lab 5 and 6 marks.xlsx".

a) Are the assumptions and conditions for inference met? Explain. [2 marks]

b) Is there a significant difference in marks (in %) between Lab 5 and Lab 6? Based on the data provided, test an appropriate hypothesis using a 10% significance level. [4 marks]

Lab Week 5 (%)
85.8
86
100
98
100
100
97
100

Lab Week 6 (%)
78
80
100
98
100
100
95.7
94.3
96.8
100
85
92.2
99.3
95.4
97
98

Randomness: The question states that a random nonagon sample of 12 students was selected. This satisfies the assumption of randomness.

Independence: The independence assumption is met when the observations within the sample are independent of each other. In this case, we assume that the marks of one student do not influence the marks of another student. As long as the students in the sample were selected independently, this assumption is met.

Sample size: Generally, a sample size of at least 30 is considered large enough to apply inference methods. In this case, we have a sample size of 12, which is smaller than 30. However, since we are not provided with any additional information, we will assume that the sample size is adequate.

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