PYC3704
Assignment 2
Unique No:733362
Due 19 November 2025
, PYC3704 – Assignment 2
Semester 2 – Unique Number: 733362
Question 1
In statistical hypothesis testing, the test statistic is used to determine the p-value,
which is compared to the chosen level of significance to make a decision about the
hypotheses.
Explanation: First, a test statistic (such as t, z, or χ²) is calculated from the sample
data. This statistic is then used to find the p-value, which indicates the probability of
obtaining results as extreme as the observed ones if the null hypothesis is true. The p-
value is compared to the pre-set significance level (α) to decide whether to reject or fail
to reject the null hypothesis.
Question 2
Two samples are considered dependent when there is a systematic relationship
between the measurements in one sample and the measurements in the other.
Explanation: Dependent samples arise when the same individuals are measured more
than once (e.g., pre-test and post-test) or when participants are matched based on
certain characteristics. This link means the observations are not independent.
Question 3
If H₀: µ = 100 is tested against H₁: µ ≠ 100 with α = 0.05, and the t-statistic is –3.20 with
a two-tailed p = 0.04, the correct decision is to reject H₀ and accept H₁.
Explanation: Since the p-value (0.04) is smaller than the significance level (0.05), the
evidence is statistically significant, and we reject the null hypothesis in favour of the
alternative hypothesis.
Question 4
A t-test variation can be used when: (a) and (c) are correct.
Explanation: T-tests are used to compare the mean of one group to a known value
(one-sample t-test) or to compare the means of two groups (independent or paired t-
Assignment 2
Unique No:733362
Due 19 November 2025
, PYC3704 – Assignment 2
Semester 2 – Unique Number: 733362
Question 1
In statistical hypothesis testing, the test statistic is used to determine the p-value,
which is compared to the chosen level of significance to make a decision about the
hypotheses.
Explanation: First, a test statistic (such as t, z, or χ²) is calculated from the sample
data. This statistic is then used to find the p-value, which indicates the probability of
obtaining results as extreme as the observed ones if the null hypothesis is true. The p-
value is compared to the pre-set significance level (α) to decide whether to reject or fail
to reject the null hypothesis.
Question 2
Two samples are considered dependent when there is a systematic relationship
between the measurements in one sample and the measurements in the other.
Explanation: Dependent samples arise when the same individuals are measured more
than once (e.g., pre-test and post-test) or when participants are matched based on
certain characteristics. This link means the observations are not independent.
Question 3
If H₀: µ = 100 is tested against H₁: µ ≠ 100 with α = 0.05, and the t-statistic is –3.20 with
a two-tailed p = 0.04, the correct decision is to reject H₀ and accept H₁.
Explanation: Since the p-value (0.04) is smaller than the significance level (0.05), the
evidence is statistically significant, and we reject the null hypothesis in favour of the
alternative hypothesis.
Question 4
A t-test variation can be used when: (a) and (c) are correct.
Explanation: T-tests are used to compare the mean of one group to a known value
(one-sample t-test) or to compare the means of two groups (independent or paired t-
