At a local Mcdonald’s managers will return a shipment of hamburger buns if more than 10% of the buns are crushed. A random sample of 81 buns 13 buns crashed. A 5% significance test is conducted to determine if the shipment should be accepted. The null and the alternative hypothesis are:

Answer 1

In this scenario, we're looking to test whether the proportion of crushed hamburger buns in a shipment is greater than 10%.

The hypotheses for this test can be defined as follows:

• Null Hypothesis (H0): The proportion of crushed buns is less than or equal to 10%. This can be mathematically stated as:
  \( H_0: p \leq 0.10 \)

• Alternative Hypothesis (H1): The proportion of crushed buns is greater than 10%. This can be mathematically stated as:
  \( H_1: p > 0.10 \)

Where \( p \) represents the true proportion of crushed buns in the shipment.

Given that in the sample of 81 buns, 13 buns were crushed, we can calculate the sample proportion of crushed buns, which would be \( \hat{p} = \frac{13}{81} \).

Now, we can conduct a hypothesis test to determine if the null hypothesis can be rejected in favor of the alternative hypothesis, using a significance level of 5%.