Chicken Delight claims that 90% of its orders are delivered within 10 minutes of the time the order is placed. A sample of 100 orders revealed that 82 were delivered within the promised time. At the .05 significance level, can we conclude that the proportion of orders delivered within the promised time is less than 90%?
a. Enter the letter corresponding to the correct null and alternate hypotheses.
A. $H_0: p \ge 90\%$
$H_1: p < 90\%$
B. $H_0: p \le 90\%$
$H_1: p > 90\%$
C. $H_0: p = 90\%$
$H_1: p \ne 90\%$
b. What is the level of significance?
c. Which test statistic will be used, z or t?
d. Enter the letter corresponding to the correct decision rule?
A. Reject $H_0$ if $t > 1.660$
B. Reject $H_0$ if $z > 1.645$
C. Reject $H_0$ if $z < -1.645$
e. Calculate the value of the test statistic. Round your answer to two decimal places.
f. Enter the letter corresponding to the correct decision regarding the null hypothesis.
A. Reject $H_0$
B. Do not reject $H_0$
g. Enter the letter corresponding to the correct answer to the question asked in the problem.
A. No, the proportion of orders delivered within the promised time is not less than 90%.
B. Yes, the proportion of orders delivered within the promised time is less than 90%.