Question

For the following question, you need to check the requirements and identify the null hypothesis, alternative hypothesis, test statistic, P-value, critical values, then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Assuming the sample is independent simple random sample. Use both the P-value method and critical value method.

In a study of Burger King driver-through orders, it was found that 264 orders were accurate and 54 were not accurate. For McDonald’s, 329 orders were found to be accurate while 33 orders were not accurate. Use a 0.05 significance level to test the claim that Burger King and McDonald’s have the same accuracy rates.

1) Test the claim using a hypothesis test

2) Test the claim by constructing an appropriate confidence interval

3) Relative to accuracy of orders, does either restaurant chain appear to be better?

Answer 1

Let p1 be the accuracy rate of Burger King and p2 be the accuracy rate of McDonald's

1) Null Hypothesis H0: p1 =p2

Alternative Hypothesis

The sample Accuracy rate for Burger King is

The sample Accuracy rate for McDonalds is

Under H0, the test statistic is

Where

The critical value of Z for 5% significance level is +/-1.96

The P-Value is 0.0022

Since p value is less than significance level, Reject H0.

Hence, at 5% Significance level, we donot have sufficient evidenec to conclude that Burger King and McDonald’s have the same accuracy rates.

2) 95% Confidence Interval

= -0.1308 < p1-p2 < -0.0292

3) Since both the limits of Confidence Interval is negative , that means the accuracy rate for Burger King is less than accurate rate of McDonalds.

Hence, McDonalds restaurant chain appear to be better relative to accuracy of orders.