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Answer :
Final answer:
To calculate the p-value, we use the t-distribution and the formula t = (X- μ) / (s / √n). We calculate the t-value for three different observed statistics and find the corresponding p-values.
Explanation:
To calculate the p-value, we need to use the t-distribution because the population standard deviation is unknown and we have a sample size of n=9. First, we calculate the t-value using the formula:
t = (X - μ) / (s / √n)
Using the given data, we can calculate the t-values as follows:
(a) t = (96.5 - 100.4) / (4.2 / √9) = -3.57
(b) t = (100.8 - 100.4) / (4.2 / √9) = 0.95
(c) t = (103.6 - 100.4) / (4.2 / √9) = 1.33
Next, we find the p-value associated with each t-value using the t-distribution table or a calculator. The p-values are:
(a) p-value ≈ 0.0061
(b) p-value ≈ 0.1800
(c) p-value ≈ 0.1070
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