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8.2 Practice Conclusions, Type I & Type II Errors Due 5/3

Last updated over 1 year ago

6 questions

Required

6

Required

4

Required

6

Required

4

Required

6

Required

4

Question 1

1.

The label on bottles of one company’s grapefruit juice say that they contain 180 milliliters (ml) of liquid. Your friend Jerry suspects that the true mean is less than that, so he takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean volume of liquid in the bottles is 179.5 ml and the standard deviation is 1.3 ml. Jerry performs a test of Ho: μ = 180 versus Ha: μ < 180, where μ is the true mean amount of liquid in this company’s bottles of grapefruit juice. The test yields a P-value of 0.0098. What conclusion would you make for each of the following significance levels?
Reusing answers is allowed.

The p value of 0.0098 < 0.05
We reject the null hypothesis
We have convincing evidence that the true mean contents of a bottle is less than 180 ml.
The p value of 0.0098 < 0.01

Alpha level of 0.05
Alpha level of 0.01

Question 2

2.

The label on bottles of one company’s grapefruit juice say that they contain 180 milliliters (ml) of liquid. Your friend Jerry suspects that the true mean is less than that, so he takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean volume of liquid in the bottles is 179.5 ml and the standard deviation is 1.3 ml. Jerry performs a test of Ho: μ = 180 versus Ha: μ < 180, where μ is the true mean amount of liquid in this company’s bottles of grapefruit juice. Describe a Type I and Type II Error in this setting:
There is only 1 answer for Type I Error and only 1 answer for Type II Error.
You will not use two answers.

We say that the contents are less than 180 ml in each bottle when really they are equal to 180 ml.
We say that the contents are equal to 180 ml in each bottle when really they are less than 180 ml.
We say that the contents are equal to 180 ml in each bottle when really they are equal to 180 ml.
We say that the contents are less than 180 ml in each bottle when they really are less than 180 ml.

Type I Error
Type II Error

Question 3

3.

The Environmental Protection Agency has determined that safe drinking water should contain no more than 1.3 milligrams per liter (mg/l) of copper, on average. To test water from a new source, you collect water in small bottles at each of 30 randomly selected locations. The mean copper content of your bottles is 1.36 mg/l and the standard deviation is 0.18 mg/l. You perform a test of Ho: μ = 1.3 versus Ha: μ > 1.3, where μ is the true mean copper content of the water from the new source. The test yields a P-value of 0.0391.
What conclusion would you make for each of the following significance levels?

The p value of 0.0391 > 0.01
We have convincing evidence that the mean copper content of bottles is greater than 1.3 mg/l.
We do not have convincing evidence that the mean copper content of bottles is greater than 1.3 mg/l.
We reject the null hypothesis
We fail to reject the null hypothesis
The p value of 0.0391 < 0.05

Alpha level of 0.05
Alpha level of 0.01

Question 4

4.

The Environmental Protection Agency has determined that safe drinking water should contain no more than 1.3 milligrams per liter (mg/l) of copper, on average.
To test water from a new source, you collect water in small bottles at each of 30 randomly selected locations. The mean copper content of your bottles is 1.36 mg/l and the standard deviation is 0.18 mg/l.
You perform a test of Ho: μ = 1.3 versus Ha: μ > 1.3, where μ is the true mean copper content of the water from the new source.
The test yields a P-value of 0.0391. Describe a Type I and Type II Error in this setting:
There is only 1 answer for Type I Error and only 1 answer for Type II Error.
You will not use two answers.

We say the bottles have more than 1.3 mg/l when really they more than 1.3 mg/l.
We say the bottles have just 1.3 mg/l when really they have more than 1.3 mg/l.
We say the bottles have just 1.3 mg/l when really they have just 1.3 mg/l.
We say the bottles have more than 1.3 mg/l when really they have just 1.3 mg/l.

Type I Error
Type II Error

Question 5

5.

A Gallup poll report revealed that 72% of teens said they seldom or never argue with their friends. Yvonne wonders if this result holds true in her large high school. So she surveys a random sample of 150 students at her school and finds that 96 of them say they rarely or never argue with friends. She uses the data to perform a test of Ho: p = 0.72 versus Ha: p ≠ 0.72, where p is the true proportion of teens in Yvonne’s school who rarely or never argue with their friends. The test yields a P-value of 0.0287. What conclusion would you make for each of the following significance levels?

We reject the null hypothesis
The p value of 0.0287 > 0.01
We do not have convincing evidence that the true proportion of teens in Yvonne’s school who rarely or never argue with their friends is different from 72%.
The p value of 0.0287 < 0.05
We have convincing evidence that the true proportion of teens in Yvonne’s school who rarely or never argue with their friends is different from 72%.
We fail to reject the null hypothesis

Alpha level of 0.05
Alpha level of 0.01

Question 6

6.

A Gallup poll report revealed that 72% of teens said they seldom or never argue with their friends. Yvonne wonders if this result holds true in her large high school. So she surveys a random sample of 150 students at her school and finds that 96 of them say they rarely or never argue with friends. She uses the data to perform a test of Ho: p = 0.72 versus Ha: p ≠ 0.72, where p is the true proportion of teens in Yvonne’s school who rarely or never argue with their friends. The test yields a P-value of 0.0287. Describe a Type I and Type II Error in this setting:
There is only 1 answer for Type I Error and only 1 answer for Type II Error.
You will not use two answers.

We claim that the proportion of HS students that say they rarely argue with their friends is equal 72% when really it is equal to 72%.
We claim that the proportion of HS students that say they rarely argue with their friends is different from 72% when it actually is different from 72%.
We claim that the proportion of HS students that say they rarely argue with their friends is equal to 72% when really it is different from 72%.
We claim that the proportion of HS students that say they rarely argue with their friends is different from 72% when really it is equal to 72%.

Type I Error
Type II Error