Question

a restaurant advertises that its burritos weigh \[250\text{ g}\]. a consumer advocacy group doubts this claim, and they obtain a random sample of \[24\] of these burritos to test if the mean weight is significantly lower than \[250\text{ g}\]. they calculate a sample mean weight of \[242\text{ g}\] and a sample standard deviation of \[12\text{ g}\]. the advocacy group wants to use these sample data to conduct a \[t\] test on the mean. assume that all conditions for inference have been met. identify the correct test statistic for their significance test.

Answer 1

The test statistic for the t-test on the mean weight of the burritos is calculated using the formula t = (\bar{X} - \mu) / (S / \sqrt{n}), resulting in a t-test statistic of -3.27.

Step-by-step explanation:

To calculate the correct test statistic for a t-test on the mean weight of burritos, when the population standard deviation is unknown, we use the formula:

t = (\bar{X} - \mu) / (S / \sqrt{n})

Where:

• \bar{X} is the sample mean weight of the burritos, which is 242 grams.
• \mu is the claimed population mean weight, which is 250 grams.
• S is the sample standard deviation of weights, which is 12 grams.
• n is the number of samples, which is 24 burritos.

Using these values, we calculate the t-test statistic as follows:

t = (242 - 250) / (12 / \sqrt{24})

t = -8 / (12 / 4.899)

t = -8 / 2.4495

t = -3.27

The t-test statistic is -3.27. This statistic will then be used to determine if there is significant evidence to suggest that the true mean weight of the burritos is lower than the advertised 250 grams.