Answer:
Part A: The null hypothesis failed to be rejected.
Part B: The null hypothesis failed to be rejected.
Step-by-step explanation:
We have an hypothesis test with null and alternative hypothesis H0: p = 0.5 versus Ha: p > 0.5, which has the test statistic z=1.15.
Part A: If the significance level is 0.05, the conclusion depends on the P-value.
If the P-value is below 5%, the null hypothesis is rejected.
The P-value for this right-tailed tes and z=1.15 is:
![P-value=P(z>1.15)=0.125](https://tex.z-dn.net/?f=P-value%3DP%28z%3E1.15%29%3D0.125)
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.
Part B: In this case, the significance level is 0.01 and, as the alternative hypothesis is defined with an unequal sign, the test is two-tailed.
This changes the way we calculate the P-value, as we need to compute the two tails.
The P-value is:
![P-value=2P(z>1.15)=0.25](https://tex.z-dn.net/?f=P-value%3D2P%28z%3E1.15%29%3D0.25)
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.