Complete question is;
Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 350 spins, 163 landed with the heads side up. Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5?
Test the relevant hypotheses using α = 0.01
Answer:
The Test result doesn't support the claim that proportion of the time the coin would land heads is not 0.5. Rather it supports the the probability to be 0.5. So the students shouldn't interpret this result as convincing evidence that the proportion of the time the coin would land heads is not 0.5
Explanation:
The hypotheses would be;
Null hypothesis; H0: p = 0.5
Alternative hypothesis; Ha: p ≠ 0.5
We are given, X = 163 and n = 350
Thus; p^ = X/n = 163/350 = 0.4657
Since we are not given standard deviation, we will use test statistic formula;
Z = (p^ - p)/(√(p(1 - p)/n)
Z = (0.4657 - 0.5)/(√(0.5(1 - 0.5)/350)
Z = -1.28
From online P-value from T-score calculator as attached, we have;
p-value = 0.201395.
Since the p-value is > 0.01, it's not significant and so we will fail to reject the null hypothesis H0.
We will conclude that the Test result supports the conclusion that p = 0.5