Tossing a coin 10,000 times! The South African mathematician John Kerrich, while
ID: 3249869 • Letter: T
Question
Tossing a coin 10,000 times! The South African mathematician John Kerrich, while a prisoner of war during World War II, tossed a coin 10,000 times and obtained 5067 heads. Is this significant evidence at the 5% level that the probability that Kerrich's coin comes up heads is not 0.5? Report the large sample z-statistics and its P- value, write a valid conclusion. Use a 99% confidence interval to find the range of probabilities of heads that would not be rejected at the 1% level. Obtain the standard error of the estimate p^Hat. The data collected included information concerning pet owner characteristics and the type of pet owned. Here is a table of counts of subjects classified by pet ownership status and education level: Test whether there is an association between Pet ownership and Education level. State the null and alternative hypotheses. Compute the test statistic and its P - value. Report your conclusion. Also conduct the test using alpha = 1% using the critical value method. Report the expected frequencies in the space provided in the accompanied table.Explanation / Answer
3)
Hypothesis:
Null hypothesis: P = 0.5
Alternative hypothesis: P 0.5
Test statistic:
n = 10000 , p = 5067 / 10000 = 0.5067
= sqrt[ P * ( 1 - P ) / n ]
= sqrt [(0.5 * 0.5) / 10000]
= 0.005
z = (p - P) /
= (.5067 - .5)/0.005
= 1.34
P value is calculated using z = 1.34
P value = 0.1802
We fail to reject the null hypothesis .
There is not sufficient evidence at the 5% level
b)
z value at 99% CI = 2.576
CI = p +/- z * sqrt(p * ( 1-p)/ n)
= 0.5 +/- 2.576 * sqrt ( (0.5 * 0.5) / 10000)
= (0.4871 , 0.5128)
c)
Standard error = sqrt[ P * ( 1 - P ) / n ]
= sqrt [(0.5 * 0.5) / 10000]
= 0.005