Question
Please show work
Suppose Nathan, an avid baseball card collector, is interested in studying the proportions of common, uncommon, and rare baschall cards found in newly purchased card packs. Each card pack contains exactly 10 baseball cards. The fine print on each pack of cards says thal, on average, 75% of tic cards in each pack are conmon, l 5% are uncommon, and 10% are rare. Nathan wishes to test the validity of this claimed distribution, so he randomly selects 20 packs of baseball cards and looks at the rarity of each of the 200 total cards. To determine if the distribation of rarity levels in his sample is significantly different than the distribution claimed on the card packs, Nathan decides to perform a chi-square test for goodness-of-fit. His results are shown in the table Rarity Observed Test proportion Expected Contribution to chi-square Common Uncommon 159 27 14 0.75 0.15 0.10 150 30 20 0.540 0.300 1800 Rare Chi square statistic: 2.6100 Degrees of freedom: 2 What is the p-valuc for Nathan's chi-square test for goodeess-of-fii? Roand your answer to three decimal places
Explanation / Answer
P value = 0.267
alfa = 0.05
p>0.05
The result is not significant.
We don't reject the null hypothesis
We can say that there is sufficient evidence to support against the claim