The management team does not want lose too much money, so they decide to test if more than 14% of deliveries take more than 45 minutes. Using a= 0.01, is there sufficient evidence to conclude that more than 14% of deliveries take longer than 45 minutes? Conduct a full hypothesis test by following the steps below.
a. Define the population parameter in context in one sentence.
b. State the null and alternative hypotheses using correct notation.
c. State the significance level for this problem.
d. Check the three conditions of the Central Limit Theorem that allow you to use the one-proportion z-test using one complete sentence for each condition. Show work for the numerical calculation. You can assume the population is large.
e. Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing your work and provide the resulting test statistic. Do not round while doing the calculation. Then, round the test statistic to two decimal places after you complete the calculation.
f. Calculate the p -value using the standard Normal table and provide the answer. Use four decimal places for the p- value.
g. State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence.
h. State your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.
