Chicken Delight claims that 86 percent of its orders are delivered within 10 minutes of the time the order is placed. A sample of 70 orders revealed that 57 were delivered within the promised time. At the .02 significance level, can we conclude that less than 86 percent of the orders are delivered in less than 10 minutes

Question

Chicken Delight claims that 86 percent of its orders are delivered within 10 minutes of the time the order is placed. A sample of 70 orders revealed that 57 were delivered within the promised time. At the .02 significance level, can we conclude that less than 86 percent of the orders are delivered in less than 10 minutes

(a) What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Reject Ho if z <

(b)
Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round sample proportion to 2 decimal places. Round your answer to 2 decimal places.)

Value of the test statistic

Answer 1

I have no idea

Answer 2

(a) To determine the decision rule for the hypothesis test, we need to find the critical value of the test statistic at the given significance level. Since the alternative hypothesis is testing for a proportion less than 86%, it is a left-tailed test.

At a significance level of 0.02, we need to find the critical value that corresponds to an area of 0.02 in the left tail of the standard normal distribution. Using a standard normal distribution table or a calculator, we find that the critical value is -2.05 (rounded to 2 decimal places).

Therefore, the decision rule is: Reject the null hypothesis if the test statistic is less than -2.05.

(b) To compute the test statistic, we first need to calculate the sample proportion. Given that a sample of 70 orders revealed that 57 were delivered within 10 minutes, the sample proportion is:

Sample Proportion (p̂) = (57/70) = 0.81 (rounded to 2 decimal places)

The test statistic for testing a proportion can be calculated using the formula:

Test Statistic (z) = (p̂ - p) / sqrt(p(1-p)/n)

Where:
p̂ is the sample proportion,
p is the hypothesized population proportion (86% or 0.86),
n is the sample size (70).

Plugging in the values, we get:

Test Statistic (z) = (0.81 - 0.86) / sqrt(0.86(1-0.86)/70)

Calculating this expression, we find: -1.97 (rounded to 2 decimal places).

Therefore, the value of the test statistic is -1.97.