Chicken Delight claims that 86 percent of its orders are delivered within 10 minutes of the time the order is placed. A sample of 80 orders revealed that 65 were delivered within the promised time. At the .10 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 your answer to 2 decimal places.)
Value of the test statistic
You can probably use a one-sample proportional test for your data. (Test sample proportion = 65/80 or .8125) Find the appropriate table for your critical value at .10 level of significance for a one-tailed test. Compare the test statistic you calculate to the critical value from the table. If the test statistic exceeds the critical value, reject the null. If the test statistic does not exceed the critical value, do not reject the null. You can draw your conclusions from there.
Chicken Delight claims that 88 percent of its orders are delivered within 10 minutes of the time the order is placed. A sample of 60 orders revealed that 50 were delivered within the promised time. At the .05 significance level, can we conclude that less than 88 percent of the orders are delivered in less than 10 minutes?
To answer this question, we need to perform a hypothesis test. The hypothesis we want to test is:
Null hypothesis (Ho): The true proportion of orders delivered within 10 minutes is equal to 86%.
Alternative hypothesis (Ha): The true proportion of orders delivered within 10 minutes is less than 86%.
Let's calculate the test statistic and the decision rule.
(a) The decision rule is based on the significance level, which is given as 0.10. It is a one-tailed test because we are testing whether the proportion is less than 86%.
To determine the decision rule, we need to find the critical value corresponding to the significance level. Since our alternative hypothesis is one-tailed (less than), we will find the critical value from the standard normal distribution for a left-tailed test.
The critical value can be found using a standard normal distribution table or a statistical software. For a significance level of 0.10, the critical value is approximately -1.28.
Therefore, the decision rule is: Reject Ho if the test statistic (z) is less than -1.28.
(b) To compute the test statistic, we need to calculate the z-score. The formula for the z-score of a proportion is:
z = (p̂ - p) / √(p(1-p) / n)
Where:
p̂ is the sample proportion (65/80 = 0.8125)
p is the hypothesized proportion (0.86)
n is the sample size (80)
Plugging in the values:
z = (0.8125 - 0.86) / √(0.86 * (1 - 0.86) / 80)
Calculating:
z = (-0.0475) / √(0.86 * 0.14 / 80) ≈ -0.765
Therefore, the test statistic is approximately -0.765.