Question

a factory fills bottles with a beverage, and each bottle is supposed to contain \[500\text{ ml}\]. norah is in charge of a quality control test that involves measuring the amounts in a sample of bottles to see if the sample mean amount is significantly different than \[500 \text{ ml}\]. she takes a random sample of \[16\] bottles and finds a mean amount of \[497\text{ ml}\] and a sample standard deviation of \[6\text{ ml}\]. norah wants to use these sample data to conduct a \[t\] test on the mean. assume that all conditions for inference have been met. calculate the test statistic for norah's test. you may round your answer to two decimal places.

Answer 1

To calculate the test statistic for Norah's test, we use the formula t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Plugging in the values, we find that the test statistic is -2.

Step-by-step explanation:

To calculate the test statistic for Norah's test, we need to use the formula:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Plugging in the values from the question, we have:

t = (497 - 500) / (6 / sqrt(16))

Simplifying the equation:

t = -3 / (6 / 4)

t = -2

Therefore, the test statistic for Norah's test is -2.