To test a certain coin for fairness, you perform a two-sided Binomial Significan

Question

To test a certain coin for fairness, you perform a two-sided Binomial Significance Test at Sigma = 1%. Out of 100 tosses you get 38 heads, thus the test fails to reject a null-hypothesized value of p = 50%. Based on this data, you now wonder what other null-hypothesized values of p would also fail to be rejected.

Use your TI-89 Binomial cdf function to solve: please show work for inputed calculations for n, p, upper value, and lower value.  

a) Find the largest whole-number percent p that the test fails to reject (include the percent P-value).

b) Find the smallest whole-number percent p that the test fails to reject (include the percent P-value). [Hint: remember to use updated values of E(X) when computing the new P-values]

Explanation / Answer

Here we are performing two sided binomial significance test at sigma = 0.01

so,

(a) if largest whole number percent value = p

then BINOMCDF (38, 100, p , true) < 0.005 (as it is two tailed test)

so here largest whole number comes out to be 51.

for p = 51%, the test fails to reject the null hypothesis.

because ; BINOMCDF (38 , 100, 0.51,, true) = 0.006

and BINOMCDF(38, 100 , 0.52, true) = 0.003

(b) Here now we will see the smallest whole number perccent p

so here we will check that BINOMCDF (38, 100, p , true) > 0.995

so now we will check it in excel.

for p = 0.27 ; BINOMCDF (38, 100, p , true) =0.994

for p = 0.26 ; BINOMCDF (38, 100, p , true) = 0.997

so here the smallest whole number percent p = 27% .

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