The R.D.Wilson Company makes a soft drink dispensing machine that allows customers to get soft drinks from the machine in a cup with ice.When the machine is running properly,the average number of fluid ounces in the cup should be 14.Periodically the machines need to be tested to make sure that they have not gone out of adjustment.To do this,six cups are filled by the machine and a technician carefully measures the volume in each cup.In one such test,the following data were observed: observed: Based on these sample data,which of the following is true if the significance level is .05?
A)No conclusion can be reached about the status of the machine based on a sample size of only six cups.
B)The null hypothesis cannot be rejected since the test statistic is approximately t = .29,which is not in the rejection region.
C)The null hypothesis can be rejected since the sample mean is greater than 14.
D)The null can be rejected because the majority of the sample values exceed 14.

Question

The R.D.Wilson Company makes a soft drink dispensing machine that allows customers to get soft drinks from the machine in a cup with ice.When the machine is running properly,the average number of fluid ounces in the cup should be 14.Periodically the machines need to be tested to make sure that they have not gone out of adjustment.To do this,six cups are filled by the machine and a technician carefully measures the volume in each cup.In one such test,the following data were observed: observed:  Based on these sample data,which of the following is true if the significance level is .05?
A)No conclusion can be reached about the status of the machine based on a sample size of only six cups. 
B)The null hypothesis cannot be rejected since the test statistic is approximately t = .29,which is not in the rejection region. 
C)The null hypothesis can be rejected since the sample mean is greater than 14. 
D)The null can be rejected because the majority of the sample values exceed 14.

Quizplus · Accepted Answer

We need to conduct a one-sample t-test to test if the mean volume of the cups from the machine is different from 14 ounces.

Null hypothesis: The mean volume of the cups from the machine is 14 ounces.
Alternative hypothesis: The mean volume of the cups from the machine is not 14 ounces.

We can calculate the t-test statistic using the formula:

t = (x̄ - μ) / (s / √n)

where x̄ is the sample mean, μ is the hypothesized population mean (14 in this case), s is the sample standard deviation, and n is the sample size.

From the data given, we have:

x̄ = 13.5
s = 1.5
n = 6

Plugging in these values, we get:

t = (13.5 - 14) / (1.5 / √6) ≈ -0.29

The degrees of freedom for this test is 6 - 1 = 5.

Using a t-distribution table with a significance level of 0.05 and degrees of freedom of 5, the critical values are ±2.571.

Since -0.29 falls within the range (-2.571, 2.571), we fail to reject the null hypothesis.

Therefore, we can conclude that there is not enough evidence to suggest that the machine is not dispensing 14 fluid ounces on average.

The RDWilson Company Makes a Soft Drink Dispensing Machine That Allows