In: Statistics and Probability
In this game, there is only one deck of cards. You play with a friend and the deck of cards belongs to him/her. Numbered cards are worth their face value, jacks are worth 11, queen 12, kings 13 and aces 14. You have a suspicion that in this deck of cards, your friend has replaced some high cards in the deck with low cards.
You take 10 cards and quickly calculate the average value: 4.5. You do the math: In a regular deck of cards the average should be mean =7.5 and standard deviation = 4.18
Ho : µ = 7.5
Ha : µ < 7.5
(Left tail test)
Level of Significance , α =
0.10
population std dev , σ =
4.1800
Sample Size , n = 10
Sample Mean, x̅ = 4.5000
Standard Error , SE = σ/√n = 4.1800 / √
10 = 1.3218
Z-test statistic= (x̅ - µ )/SE = (
4.500 - 7.5 ) /
1.3218 = -2.27
p-Value = 0.0116 [
Excel formula =NORMSDIST(z) ]
Decision: p-value<α, Reject null hypothesis
Conclusion: There is enough evidence that card have been
replaced.
If you would like to be even more confident in your statement and use a significance level of 1%, which corresponds to being 99 percent confident,
We would you need a lower p-value to reject the Null hypothesis
For 99% confidence , Level of Significance , α = 0.01
p-Value = 0.0116 [
Excel formula =NORMSDIST(z) ]
Decision: p-value>α, Do not Reject null
hypothesis
Thanks in advance!
revert back for doubt
Please upvote