Suppose that George has tossed a coin 52 times. The number of heads and tails wh
ID: 3181899 • Letter: S
Question
Suppose that George has tossed a coin 52 times. The number of heads and tails which resulted are shown below.
a. Assuming the coin is "fair" (i.e., the probability of a head and a tail is equal), compute the expected frequencies for each outcome.
Enter your expected frequencies as whole numbers.
Expected number of heads =
Expected number of tails =
b. After seeing the results, George claims the coin is not fair. He wants to conduct a chi-square goodness-of-fit test to investigate it further. Select the appropriate null hypothesis and alternative hypotheses.
H0:
Ha:
c. Compute the value of the chi-square test statistic.
Round your intermediate chi-square terms to three decimal places. Round your answer to three decimal places.
Chi-square test statistic =
d. Determine the appropriate critical value at the 10% significance level.
Enter your critical value to three decimal places.
Critical value =
e. Select the appropriate initial conclusion.
f. Select the appropriate final conclusion.
Outcome Heads Tails Frequency 30 22Explanation / Answer
The statistical software output for this problem is:
Chi-Square goodness-of-fit results:
Observed: Frequency
Expected: All cells in equal proportion
So,
a) Expected number of heads = 26
Expected number of tails = 26
b) H0: The coin is fair.
H1: The coin is not fair.
c) Test statistic = 1.231
d) Critical value = Chi - square value at 1 degree of freedom and 0.1 significance level = 3.841
e) Do not reject the null hypothesis.
f) Do not support the claim that the coin is unfair.
N DF Chi-Square P-value 52 1 1.2307692 0.2673