To solve this hypothesis test, we need to compute the p-value and state our conclusion for each of the given sample results. Let's go through each sample result one by one:
(a) p = 0.78
To compute the p-value, we will use the appropriate appendix table or technology. Since the alternative hypothesis is one-sided (p < 0.85), we will look up the z-score corresponding to the observed p of 0.78. Once we have the z-score, we can find the corresponding p-value.
After finding the p-value, we compare it to the significance level (α = 0.05) to make our conclusion. If the p-value is less than α, we reject the null hypothesis. If the p-value is greater than or equal to α, we fail to reject the null hypothesis.
(b) p = 0.83
Again, we will compute the p-value using the same process as in part (a). Look up the z-score corresponding to the observed p of 0.83, find the corresponding p-value, and compare it to the significance level (α = 0.05).
(c) p = 0.80
Repeat the same process as before. Compute the p-value using the observed p of 0.80, compare it to the significance level (α = 0.05), and draw your conclusion accordingly.
(d) p = 0.88
Once again, compute the p-value using the observed p of 0.88, compare it to the significance level (α = 0.05), and make your conclusion.
Remember, the p-value represents the probability of obtaining a sample result as extreme as or more extreme than the one observed, assuming the null hypothesis is true. If the p-value is small, it suggests that the observed result is unlikely under the null hypothesis and provides evidence against it. On the other hand, if the p-value is large, it indicates that the observed result is likely under the null hypothesis, and we fail to find evidence against it.
By following these steps for each sample result, you can compute the p-value and make a conclusion for this hypothesis test.