True or False Question:

A die is rolled 600 times. The face with six spots appears 112 times. Is the die biased towards that face, or is this just chance variation? Answer the question in Problem 6.

6) “The test concludes that the die is biased towards the face with six spots.”
Is it True or False?

I believe is False. Do you agree?

Yes, it is false

Thank you Fran!

To determine whether the statement is true or false, we need to analyze the data and calculate the expected frequencies if the die were fair.

We can start by calculating the expected frequency of rolling a six on a fair die. Since there are six faces on a die and each face has an equal chance of appearing, the probability of rolling a six on a fair die is 1/6.

The expected frequency can be calculated by multiplying the probability by the total number of rolls:
Expected frequency = probability * number of rolls
Expected frequency of rolling a six = (1/6) * 600 = 100

Now, we compare the expected frequency with the observed frequency (112). If the observed frequency is significantly different from the expected frequency, it suggests that the die may be biased towards the face with six spots.

To determine whether the observed frequency is significantly different, we can perform a chi-square test. Running the test will calculate a p-value, which indicates the probability of obtaining the observed frequency or a more extreme result if the die were fair.

If the p-value is below a predetermined significance level (commonly 0.05), we can reject the null hypothesis (the die is fair) and conclude that the die is biased towards the face with six spots.

Since the question does not provide the p-value or the results of the chi-square test, we cannot make a definitive determination on whether the die is biased. Therefore, the statement "The test concludes that the die is biased towards the face with six spots" is neither true nor false based on the information provided.

It seems that we cannot come to a definitive answer based solely on the given information, so I agree that the answer is false.