A coin was flipped 13 times and came up heads 10 times. (a) The assumption of no

Question

A coin was flipped 13 times and came up heads 10 times.

(a) The assumption of normality is justified.

No

Yes

(b-1)

Calculate a p-value for the observed sample outcome, using the normal distribution. (Round your z-value to 2 decimal places. Round your answer to 4 decimal places.)

p-value

(b-2) At the 0.05 level of significance in a right-tailed test, is the coin biased toward heads?

Yes

No

(c)

Use Excel to calculate the binomial probability P(X 10 | n = 13, formula96.mml = 0.50) = 1 P(X 9 | n = 13, formula96.mml = 0.50). (Round your answer to 4 decimal places.)

P(X 10)

(d) The normal probability is

An approximation.

The same as the binomial probability.

Explanation / Answer

Ans:

a)not ,justified.(as n<30,sample size is not large)

Large sample size: sample size needs to be sufficiently large.
Central Limit Theorem

b)sample proportion=10/13=0.7692

z=( 0.7692-0.5)/sqrt(0.5*0.5/13)=1.941

p-value=P(z>1.941)=0.0261

As,p-value<0.05,we reject null hypothesis.

There is sufficient evidence that coin is biased towards heads.(Yes)

c)P(X>=10)=1-P(X<=9)=1-BINOMDIST(9,13,0.5,TRUE)=0.0461

d)Probability in part is different from part b ,as sample size is very small,so not a good approximation.

Normal probability is an approximation.

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