A coin was flipped 15 times and came up heads 10 times. (a) The assumption of no

Question

A coin was flipped 15 times and came up heads 10 times. (a) The assumption of normality is justified. No Yes Calculate a p-value for the observed sample outcome, using the normal distribution. At the 0.05 level of significance in a right-tailed test, is the coin biased toward heads? No Yes (c) Use Excel to calculate the binomial probability P(X greaterthanorequaklto 10 | n = 15, pi = 0.50) = 1 - P(X lessthanorequalto 9 | n = 15, pi = 0.50). (Round your answer to 4 decimal places.) (d)The normal probability is An approximation. The same as the binomial probability.

Explanation / Answer

a. For assumption of normality to hold true, both np and nq should be atleast 10, where, n is sample size, and p is probability of success, and q is probability of failure, q=(1-p).

Here, n=15 independent trials, p=0.5

Therefore, np=15*0.5=7.5, and nq=15*(1-0.5)=7.5.

The assumption doesnot hold.

b-1 Compute Z test statistic using following formula and then obtain p value.

Z=(phat-p)/sqrt[p(1-p)/n], where, phat is sample proportion, p is population proportion, n is sample size.

=(10/15-0.5)/sqrt[0.5(1-0.5)/15]

=1.29

P value: 0.0985

b-2 The p value for right-tailed test is 0.0985. The coin should be declared biased, if p value is less than 0.05. But the p value is not less than 0.05, therefore, fail to cocnclude that coin is biased towards head.

c. Type: =1-BINOMDIST(9,15,0.5,TRUE) in the formula bar. Ans>0.1509.

d. The normal probability is an approximation to the binomial probability, they donot hold exactly same value.

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