The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose that 800 jawbreakers are selected at random form the production lines. Would it be unusual for this sample of 800 to contain 386 jawbreakers that weigh more than .4 ounces? Explain
60% of 800 = 480
so, is 386 less than 480?
no
so is it unusual for this sample?
1/5 and 881 ounces.
To determine if it would be unusual for a sample of 800 jawbreakers to contain 386 jawbreakers that weigh more than 0.4 ounces, we need to compare the observed proportion to the expected proportion based on the given claim.
We are told that the Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than 0.4 ounces. This means that, according to their claim, the proportion of jawbreakers weighing more than 0.4 ounces is 0.60, or 60%.
To determine the expected number of jawbreakers weighing more than 0.4 ounces in the sample of 800, we can multiply the sample size by the expected proportion:
Expected number = sample size * expected proportion
Expected number = 800 * 0.60
Expected number = 480
So based on the company's claim, we would expect around 480 jawbreakers to weigh more than 0.4 ounces in the sample of 800.
Now, to determine if it would be unusual, we need to assess whether the observed number, which is 386, is significantly different from the expected number of 480.
One way to assess this is by using statistical hypothesis testing, specifically a binomial test. However, this typically requires additional information, such as the significance level or the assumption of a normal distribution. Since these details are not provided, we cannot perform a formal hypothesis test.
Nevertheless, we can still make a qualitative judgment. If the observed number is close to the expected number, it would not be considered unusual. However, if the observed number deviates significantly from the expected number, it would be considered unusual.
In this case, the observed number of 386 is somewhat lower than the expected number of 480, but without explicitly calculating the p-value or applying a significance level, we cannot definitively classify it as unusual or not. It would be best to consult with a statistician or conduct a formal statistical test to make a conclusive determination.