Question

I wrote this for a simple experiment assignment relating two variables; yet the more i wrote the more confused i became lol. Does this paragraph make sense? specifically the math i used. i always thumbs up helpful answers; Thank you!

"In this experiment, we flipped a coin to see how many times it
would land on either heads or tails. The H_{O} for this
experiment suggests that this quarter is standard mint issue
(p=0.5); the H_{A} states that the quarter is two sided for
tails (p>0.5). The flipping of a coin is an art form dealing
primarily, with dichotomous variables; essentially a yes or no
option. When flipping a coin, the probability of landing on heads
or tails (the p-value) stays at 0.5 (independent) and does not
change despite how many times you flip the coin. The event of the
coin landing on either one of these however, is dependent on the
coin being flipped. These dichotomous variables are considered a
type, or sublevel, of nominal variables, suggesting no intrinsic
order and only two available output categories. We tossed the coin
a total of 10 times, 8 of those landed on tails; assuming a
binomial distribution of n=10, p=0.5 and a “small p-value” being
deemed lower than 0.05, we must conclude that the null is false
where as the alternative is true.

p[8]+p[9]+p[10] = 0.044+0.01+0.001 = 0.055 > 0.05"

Answer #1

" When flipping a coin, the probability of landing on heads or
tails (the **p-value**) stays at 0.5 (independent) and
does not change despite how many times you flip the coin. "

-That isn't what a p-value means. I would omit calling it a p-value

-You later use the p-value for the statistic from the sample where 8 tails appeared. This usage of p-value is also incorrect. P-value isn't just the probability of the observing the data you observed.

P-value is the probability of observing data that is AT LEAST as extreme as the data you observed, given the null is true. So, p-value here would be the probability that we observe 8 or more tails, when the null is assumed to be true. P-value=0.055. So we would not reject the null hypothesis at 5% significance level.

You are mostly thinking correctly, but your understanding of what p-value is is lacking. I would suggest to look more thoroughly at it.

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