STAT 300 - College 4.3 Exam UPDATED
QUESTIONS AND CORRECT ANSWERS
Quality control is an important aspect of the manufacturing process. Suppose a local company
manufactures soda-dispensing machines that fill bottles with 600 ml of soda.
Over time, the dispensing machines can become less precise. That is, older machines may dispense
too much or too little soda into the bottles.
When something becomes less precise, we say that it has lost its precision. When this occurs, the
machine requires an adjustment. In this case, a soda dispensing machine will need adjustment if the
mean amount of soda dispensed is different than 600 ml. - CORRECT ANSWER The owner of
one soda dispensing machine believes that her machine has lost precision. She measures the amount
of soda dispensed at eight random times throughout the day. The eight amounts of soda her machine
dispensed during the day are listed below:
600.15
599.92
599.85
599.92
599.81
600.14
600.04
599.98 - CORRECT ANSWER At 5% level of significance, is there sufficient evidence to
conclude that this machine needs an adjustment? Research has indicated that the amounts of soda
dispensed from the machine are approximately normal in their distribution.
Complete the steps below.
Step 1: Determine the Hypotheses
State the null hypothesis. - CORRECT ANSWER 600. The null hypothesis is that μ=600
State the alternative hypothesis. - CORRECT ANSWER ≠. The alternative hypothesis is that
μ≠600
The statement "...older machines may dispense too much or too little soda into the bottles" makes this
a two-tailed test. We are investigating whether the mean amount of soda dispensed by the machine is
different than 600 ml.
, Are the criteria for the approximate normality of the sampling distribution of sample means
satisfied?.. - CORRECT ANSWER Yes, since the sample is taken from a normally distributed
population.
Yes, since the sample is taken from a normally distributed population. In order to satisfy the normality
criteria, the sample size needs to be greater than 30, or the sample must be drawn from a normally
distributed population. The statement, "Research has indicated that the amounts of soda dispensed
from the machine are approximately normal in their distribution" allows us to conclude that the
sample is drawn from a normally distributed population.
Use technology to calculate the sample mean. Round your answer to two decimal places.
x¯= - CORRECT ANSWER 599.98
Use technology to calculate the sample standard deviation. Round your answer to three decimal
places.
s = - CORRECT ANSWER 0.126
Calculate the test statistic for the observed sample mean. Round your answer to two decimal places.
T =... - CORRECT ANSWER -0.45.
599.98 -
600/ 0.126/
sq root of 8 =
Use the test statistic to find the P-value, rounded three places after the decimal.
P-value =
Use technology to find the P-value. Be sure to use the T-distribution set to the appropriate degrees of
freedom. This is a two-tailed test. The Desmos calculator found here can be used to find P-values in a
T-distribution. Specify the degrees of freedom and the test statistic, and use the area in a tail to find
the P-value. - CORRECT ANSWER 0.666. Since this is a two-tailed test, and since the test
QUESTIONS AND CORRECT ANSWERS
Quality control is an important aspect of the manufacturing process. Suppose a local company
manufactures soda-dispensing machines that fill bottles with 600 ml of soda.
Over time, the dispensing machines can become less precise. That is, older machines may dispense
too much or too little soda into the bottles.
When something becomes less precise, we say that it has lost its precision. When this occurs, the
machine requires an adjustment. In this case, a soda dispensing machine will need adjustment if the
mean amount of soda dispensed is different than 600 ml. - CORRECT ANSWER The owner of
one soda dispensing machine believes that her machine has lost precision. She measures the amount
of soda dispensed at eight random times throughout the day. The eight amounts of soda her machine
dispensed during the day are listed below:
600.15
599.92
599.85
599.92
599.81
600.14
600.04
599.98 - CORRECT ANSWER At 5% level of significance, is there sufficient evidence to
conclude that this machine needs an adjustment? Research has indicated that the amounts of soda
dispensed from the machine are approximately normal in their distribution.
Complete the steps below.
Step 1: Determine the Hypotheses
State the null hypothesis. - CORRECT ANSWER 600. The null hypothesis is that μ=600
State the alternative hypothesis. - CORRECT ANSWER ≠. The alternative hypothesis is that
μ≠600
The statement "...older machines may dispense too much or too little soda into the bottles" makes this
a two-tailed test. We are investigating whether the mean amount of soda dispensed by the machine is
different than 600 ml.
, Are the criteria for the approximate normality of the sampling distribution of sample means
satisfied?.. - CORRECT ANSWER Yes, since the sample is taken from a normally distributed
population.
Yes, since the sample is taken from a normally distributed population. In order to satisfy the normality
criteria, the sample size needs to be greater than 30, or the sample must be drawn from a normally
distributed population. The statement, "Research has indicated that the amounts of soda dispensed
from the machine are approximately normal in their distribution" allows us to conclude that the
sample is drawn from a normally distributed population.
Use technology to calculate the sample mean. Round your answer to two decimal places.
x¯= - CORRECT ANSWER 599.98
Use technology to calculate the sample standard deviation. Round your answer to three decimal
places.
s = - CORRECT ANSWER 0.126
Calculate the test statistic for the observed sample mean. Round your answer to two decimal places.
T =... - CORRECT ANSWER -0.45.
599.98 -
600/ 0.126/
sq root of 8 =
Use the test statistic to find the P-value, rounded three places after the decimal.
P-value =
Use technology to find the P-value. Be sure to use the T-distribution set to the appropriate degrees of
freedom. This is a two-tailed test. The Desmos calculator found here can be used to find P-values in a
T-distribution. Specify the degrees of freedom and the test statistic, and use the area in a tail to find
the P-value. - CORRECT ANSWER 0.666. Since this is a two-tailed test, and since the test
