Question

A factory fills bottles with a beverage, and each bottle is supposed to contain 500\text{ mL}500 mL500, start text, space, m, L, end text. 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 ml. She takes a random sample of 16 bottles and finds a mean amount of 497ml, and a sample standard deviation of 6ml. Norah wants to use these sample data to conduct a ttt test on the mean. Assume that all conditions for inference have been met.

Required:
Calculate the test statistic for Norah's test.

Answer 1

Answer: -2

Step-by-step explanation: Khan

Answer 2

The test statistic for Norah's test is
`t = -2`

Explanation:

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 ml.

This means that at the null hypothesis we test if the sample mean is 500 ml, that is:

`H_0: \mu = 500`

At the alternate hypothesis, we test if it is differente than 500 ml, that is:

`H_a: \mu \\eq 500`

The test statistic is:

`t = (X - \mu)/((s)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

500 is tested at the null hypothesis:

This means that
`\mu = 500`

She takes a random sample of 16 bottles and finds a mean amount of 497ml, and a sample standard deviation of 6ml.

This means that
`n = 16, X = 497, s = 6`

Calculate the test statistic for Norah's test.

`t = (X - \mu)/((s)/(√(n)))`

`t = (497 - 500)/((6)/(√(16)))`

`t = -2`

The test statistic for Norah's test is
`t = -2`