Question

Test the claim that your coin is fair, using a 5% level of significance. Use the Chi-Square Goodness of Fit Test.

Toss a coin at least 12 times (why?).

a) What is n? What are the number of Tails and Heads? These are the Observed frequencies.

b) What are the Expected frequencies?

c) What is the Null Hypothesis H0?

d) What is the Alternative Hypothesis H1?

e) Is this a left, right, or two-tailed test?

f) Chi-Square Test Statistic =?

g) P-value =?

h) Compare the p-value and alpha. Do you reject the Null or do you fail to reject the Null?

i) What is the final conclusion of the test? This is always a complete sentence.

So you have tested if a coin is fair in 3 ways--confidence interval (Week 9 Discussion), Hypothesis Test for Proportions (Week 11 Discussion), and now, a Chi-Square Hypothesis Test. Which test is the most reliable and which one would you use?

Answer 1

n = No. of time we loss the coin = 12 No. of tails = 5 No. of heads = 7 fe probability of head = prob.of taileo's Expected frequence = n. Pi | Exp C Tail) = 12x0.5 = 6 Head) = 12x0.5 = 6. c) Null hypothesis :- i.f. coin is fair P= 0.5 d) Alternative hypothesis is coin is not pair_ e) It is right failed test. f Test statistic 2 = { [0; -E;) 27 ~ 7o. CE; II (0i-E;) 27 = (5-6) 2 (7-6) ² = 0.3333 P-value = 0.563 7 (Obtained using excel = CHIDISI (0.3333, 1)] P-value is we fail to greater reject Ho. than 2=0.05, hence

Date - At 5% coin is level of significance we conclude that Fair.