Question

A machine is designed to fill containers with 16 ounces of coffee. A consumer suspects that the machine is not filling the containers completely and the amount of coffee is less than 16 ounces when filled. A sample of 8 containers has a mean of 15.6 ounces of coffee and a standard deviation of 0.3 ounces of coffee.  Assume that the distribution of data is normal. At 10% significance level, is there enough evidence to support the consumer’s suspicion that the machine is not filling the containers completely and the amount of coffee in a container is less than 16 ounces when filled?

Question: Which of the following is the correct calculator command to use?

2-SampTTest

2-SampTInt

ANOVA

Z-Test

2-SampZTest

T-Interval

Z-Interval

2-SampZint

T-Test

Answer 1

Here in this Question we have to use One sample T test (T test) .

In this scenario  machine is designed to fill containers with 16 ounces of coffee. A consumer suspects that the machine is not filling the containers completely and the amount of coffee is less than 16 ounces when filled.

A sample of 8 containers has a mean of 15.6 ounces of coffee and a standard deviation of 0.3 ounces of coffee.

Here claim is that,

Claim : the coffee is filling the cup less than 16 ounces.

To test this claim we have to use the One sample T test, because here population standard deviation is unknown. I.e we estimate the sample Standerd deviation and also sample size is less than 30 . So we have to use one sample t test to test claim at 10 % level of significance.

*)) test is the test where we have to compare one sample mean to our hypothysed mean. In this scenario our hypothysed mean is 16 ounce and sample mean is 15.6 . (T test)

This is not appropriate to use z test here because the sample size is not large enough.also the population standard deviation is unknown.

Here ANOVA is also not appropriate test for this scenario because ANOVA is used to compare the mean of the three groups or more than three groups.

Others tests or calculator command are not used in this scenario.

Hope you understood.

Thank you,

Further for better understanding i performed one sample t test as below,

from the above test,

It is concluded that the amount of coffee filled by machine is less than 16 ounces at 10% level of significance.

Thank you.