Answer: a) -0.2252, b) 0.8219
Step-by-step explanation:
Since we have given that
Sample size n = 100
Probability that candies are blue = p= 0.26
Probability that company claims that it is blue candy = P = 0.27
So, Q = 1-P= 1-0.27 = 0.73
So, Null hypothesis : ![H_0:p=P](https://tex.z-dn.net/?f=H_0%3Ap%3DP)
Alternate hypothesis : ![H_1:p\neq P](https://tex.z-dn.net/?f=H_1%3Ap%5Cneq%20P)
So, the test statistic would be
![z=\dfrac{p-P}{\sqrt{\dfrac{P.Q}{n}}}\\\\z=\dfrac{0.26-0.27}{\sqrt{\dfrac{0.27\times 0.73}{100}}}\\\\z=-0.2252](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bp-P%7D%7B%5Csqrt%7B%5Cdfrac%7BP.Q%7D%7Bn%7D%7D%7D%5C%5C%5C%5Cz%3D%5Cdfrac%7B0.26-0.27%7D%7B%5Csqrt%7B%5Cdfrac%7B0.27%5Ctimes%200.73%7D%7B100%7D%7D%7D%5C%5C%5C%5Cz%3D-0.2252)
Since α = 0.05
So, critical value of z = 1.96
p-value = P(Z>Z(calculated)
Using the excel function , we get that
![P(z>0.2252)\\\\=2\times 0.410.911845\\\\=0.8219](https://tex.z-dn.net/?f=P%28z%3E0.2252%29%5C%5C%5C%5C%3D2%5Ctimes%200.410.911845%5C%5C%5C%5C%3D0.8219)
Hence, a) -0.2252, b) 0.8219