Question

In: Statistics and Probability

You perform a hypothesis test on the claim that the volume in all 12-ounce cans of...

You perform a hypothesis test on the claim that the volume in all 12-ounce cans of Fizzy Pop is less than 12 ounces. In terms of the possible conclusions of this hypothesis test, choose the appropriate description of a Type I and Type II error.

(a) If you make a Type I error, then which of the following is true?

You conclude that the mean volume is 12 ounces when it isn't.

You conclude the mean volume in all cans is less than 12 ounces when that is not true.     

You don't conclude the mean volume in all cans is less than 12 ounces when in fact, the mean volume is less than 12 ounces.


(b) A Type II error occurs when which of the following is true?

You conclude the mean volume in all cans is less than 12 ounces when that is not true.

You don't conclude the mean volume in all cans is less than 12 ounces when in fact, the mean volume is less than 12 ounces.    

You conclude that the mean volume is 12 ounces when it isn't.


(c) What is the probability of a Type I error if the significance level is α?

α
1 − 2α    
1 − α
2α

Solutions

Expert Solution

Answer:

Given that:

You perform a hypothesis test on the claim that the volume in all 12-ounce cans of Fizzy Pop is less than 12 ounces.

We make type I error,when we reject ,but in fact, is true.

We make type II error,when we fail to reject ,but in fact,  is false

a) If you make a Type I error, then which of the following is true?

You conclude the mean volume In all cans Is less than 12 ounces when that Is not true.

b) A Type II error occurs when which of the following is true?

You conclude that the mean volume Is 12 ounces when It Isn't.

c) What is the probability of a Type I error if the significance level is α?

P(type I error)=alpha

Correct option is:

orchestra answered 2 years ago
Next > < Previous

Related Solutions

You perform a hypothesis test on the claim that the volume in all 12-ounce cans of...
You perform a hypothesis test on the claim that the volume in all 12-ounce cans of Fizzy Pop is less than 12 ounces. In terms of the possible conclusions of this hypothesis test, choose the appropriate description of a Type I and Type II error. (a) If you make a Type I error, then which of the following is true? You conclude that the mean volume is 12 ounces when it isn't. You conclude the mean volume in all cans...
You are conducting a multinomial hypothesis test ( α = 0.05) for the claim that all...
You are conducting a multinomial hypothesis test ( α = 0.05) for the claim that all 5 categories are equally likely to be selected. Category Observed Frequency A 23 B 17 C 13 D 19 E 5 What is the chi-square test-statistic for this data? χ2=χ2= What are the degrees of freedom for this test? d.f. = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal...
you will propose a hypothesis test that will test a claim that is of interest to...
you will propose a hypothesis test that will test a claim that is of interest to you in the business world. Then describe how you would gather a representative sample to test that claim. 1. state the claim you wish to investigate in your own words. 2. write a null and alternative hypothesis. 3. describe how you will gather a representative sample to test your claim. 4. state the type of test you would use for example, TTest,1PropZTest, etc.
Perform the appropriate hypothesis test for the problem. State the hypotheses, identify the claim, compute the...
Perform the appropriate hypothesis test for the problem. State the hypotheses, identify the claim, compute the test statistic and P-value, make a decision, and write the interpretation in terms of the claim. For consistency, use a significance level of 0.05 for the problem. Two brands of components are compared by installing one of each brand randomly in the right and left sides of several randomly selected machines and noting the total machine operation time (in minutes) until the component needs...
Perform the appropriate hypothesis test for the problem. State the hypotheses, identify the claim, compute the...
Perform the appropriate hypothesis test for the problem. State the hypotheses, identify the claim, compute the test statistic and P-value, make a decision, and write the interpretation in terms of the claim. For consistency, use a significance level of 0.05 for the problem. Two brands of components are installed in a random sample of machines and the total machine operation time (in minutes) until the component needs to be replaced is recorded. Can you conclude that Brand 1 has a...
In a plant that fills 12 ounce cans of soda, the mean fill amount with the...
In a plant that fills 12 ounce cans of soda, the mean fill amount with the current machinery is 12.2 ounces with a standard deviation of 0.03 ounces. A new machine is said to be more accurate, so the company tested this new machine on a run of 10 cans, and obtained the following fill amounts: 12.03 12.10 12.02 11.92 12.10 12.00 12.05 11.97 11.99 11.87 Test the claim that the standard deviation of the new machine is lower than...
Perform and document a two-sample hypothesis test to evaluate the claim "American cars of the past...
Perform and document a two-sample hypothesis test to evaluate the claim "American cars of the past have a significantly different weight than non-americas cars of the past." Document all seven of the hypothesis testing steps. Data from my calculations: American Sample MPG X-Bar= 20.12 S= 6.36 N=247 Horsepower X-bar= 119.74 S=39.73 N=248 Not American Sample MPG X-bar=29.22 S=6.67 N=151 Horsepower X-bar=80.93 S=22.12 N=152 Data from both American and non American samples (if needed): MPG Mean/X-bar= 23.57 Standard Deviation= 7.84 Count=...
Most soda cans list the volume of soda as 12 fluid ounces. As with all process,...
Most soda cans list the volume of soda as 12 fluid ounces. As with all process, some variation occurs when filling soda cans. Suppose that a company knows this and tries to over-fill cans a bit, so that the actual volume of soda in a can follows a normal distribution with mean 12.1 fluid ounces and standard deviation .15 fluid ounces. a) What proportion of soda cans filled by this process will contain less than 12 fluid ounces? (In other...
A Coca-Cola bottling plant's product line includes 12-ounce cans of Coke products. The cans are filled...
A Coca-Cola bottling plant's product line includes 12-ounce cans of Coke products. The cans are filled by an automated filling process that can be adjusted to any mean filll volume and that will ll cans according to a normal distribution. However, not all cans will contain the same volume due to variation in the filling process. Historical records show that regardless of what the mean is set at, the standard deviation in ll will be 0.035 ounce. Operations managers at...
Suppose that you wish to use a hypothesis test to test a claim made by a...
Suppose that you wish to use a hypothesis test to test a claim made by a juice bottling company regarding the mean amount of juice in its 16 oz bottles. The company claims that the mean amount of juice in its 16 oz bottles is 16 oz, while you suspect the true mean is lower. You obtain n = 15 bottles of juice and find a sample mean of x¯ = 15.42 oz with a sample standard deviation of s...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT