Question

Scenario 1: Researchers are interested in estimating the

average calorie consumption of people in a specific
community and also want to know if the average differs
from the recommended 2,000 calories per day. So they
collect a random sample of people from the community
and calculate the mean and standard deviation of the
sample.

Question 3

For the random sample of 18 people from the community,
the mean daily consumption is 1,791 calories and the
standard deviation is 221 calories.
What is the critical t value for this analysis, assuming
a = 0.05? Report to 2 decimal places.

Answer 1

The critical t value for the given scenario with an alpha level of 0.05 and 17 degrees of freedom is 2.11.

Step-by-step explanation:

To find the critical t value for this analysis given an alpha (α) level of 0.05 and a sample size of 18, we must first determine the degrees of freedom.

The degrees of freedom (df) are calculated as the sample size minus one, which in this case is 18 - 1 = 17.

We then look up the critical t value for a two-tailed test with 17 degrees of freedom at the 0.05 significance level.

According to the t-distribution table or using a calculator's inverse t function, the critical t value for df = 17 at an α level of 0.05 (for both tails) is approximately 2.11 (t = invT(0.975, 17)).

The t distribution is used here because the population standard deviation is unknown and the sample size is relatively small.

Therefore, the critical t value is 2.11 when rounding to two decimal places.