JUNIORS ONLY 8.3 & 8.5 Practice Due Mon. 5/13 midnight

Last updated almost 2 years ago

12 questions

Required

3

Required

3

Required

3

Required

5

Required

5

Required

3

Required

5

Required

4

Required

5

Required

3

Required

4

Required

1

Library

JUNIORS ONLY 8.3 & 8.5 Practice Due Mon. 5/13 midnight

Last updated almost 2 years ago

12 questions

Required

3

Required

3

Required

3

Required

5

Required

5

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. 
Jason chooses an SRS of 60 students and finds that 41 have a computer at home. 
He would like to carry out a test at the α = 0.05 significance level.

What is the sample proportion? _______ round to 3 places past the decimal.
What is the mean for the sampling distribution of sample proportions? _______ Remember to use the value from the null hypothesis.
What is the standard deviation for the sampling distribution of sample proportions (the standard error)?  _______ Round to 3 places past the decimal.
What is the standardized test statistic, the z statistic? _______  Round to 2 places past the decimal.
Using the Z chart (blue) what is the probability of getting the sample results, assuming the null hypothesis is true?
P-value = _______ 

Required

3

Required

5

Required

4

At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces.
A new irrigation system was installed in this field after the growing season. Managers wonder if the mean weight of pineapples grown in the field this year will be greater than last year.  So they take an SRS of 50 pineapples from this year’s crop.

The managers want to perform a test at the α = 0.10 significance level to see if the pineapples this year are heavier.
They found the sample mean weight from this year’s crop was 31.4 ounces and the sample standard deviation was 2.5 ounces.

What is the sample mean? _______ keep all decimal places
What is the mean of the sampling distribution of sample means? _______ 
What is the standard deviation for the sampling distribution of the mean? _______ Round to 3 places past the decimal. See 8.5 for the formula if needed.
Calculate the standardized test statistic (the t statistic) _______ round to 4 places
 .   

Required

5

At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces.
A new irrigation system was installed in this field after the growing season. Managers wonder if the mean weight of pineapples grown in the field this year will be greater than last year.  So they take an SRS of 50 pineapples from this year’s crop.

The managers want to perform a test at the α = 0.10 significance level to see if the pineapples this year are heavier.
They found the sample mean weight from this year’s crop was 31.4 ounces and the sample standard deviation was 2.5 ounces.

Degrees of freedom = _______  
What degrees of freedom will you use on the t chart? _______ 
Is this a one tailed or a two tailed test? Enter 1 or 2 _______ 
Use the absolute value of the test statistic.
What are the two percentages that correspond to these values? Enter in the same order
 _______   to  _______

Required

3

Required

4

Required

1

Identify Type I and Type II Errors in this situation:
Use each answer once.

We think the pineapples are heavier this year and decide to continue using the new irrigation system when the pineapples are actually the same weight, 31 oz, so the new irrigation system did not help.
We think the pineapples are 31 oz and do not use the new irrigation system when it really did help grow heavier pineapples.

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school.
Jason chooses an SRS of 60 students and finds that 41 have a computer at home.
He would like to carry out a test at the α = 0.05 significance level.

Will this be a significance test of a proportion or of a mean.
How do you know?
What parameter are we interested in?

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school.
Jason chooses an SRS of 60 students and finds that 41 have a computer at home.
He would like to carry out a test at the α = 0.05 significance level.

Identify the null and alternative hypothesis.
Define the parameter of interest.

At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces.
A new irrigation system was installed in this field after the growing season. Managers wonder if the mean weight of pineapples grown in the field this year will be greater than last year. So they take an SRS of 50 pineapples from this year’s crop.
The managers want to perform a test at the α = 0.10 significance level to see if the pineapples this year are heavier.

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school.
Jason chooses an SRS of 60 students and finds that 41 have a computer at home.
He would like to carry out a test at the α = 0.05 significance level.

Confirm that the conditions for conducting a significance test for a mean have been met.

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. 
Jason chooses an SRS of 60 students and finds that 41 have a computer at home. 
He would like to carry out a test at the α = 0.05 significance level.

What is the sample proportion? _______ round to 3 places past the decimal.
What is the mean for the sampling distribution of sample proportions? _______ Remember to use the value from the null hypothesis.
What is the standard deviation for the sampling distribution of sample proportions (the standard error)?  _______ Round to 3 places past the decimal.
What is the standardized test statistic, the z statistic? _______  Round to 2 places past the decimal.
Using the Z chart (blue) what is the probability of getting the sample results, assuming the null hypothesis is true?
P-value = _______ 

At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces.
A new irrigation system was installed in this field after the growing season. Managers wonder if the mean weight of pineapples grown in the field this year will be greater than last year.
Will this be a significance test of a proportion or of a mean.
How do you know?
What parameter are we interested in?

At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces.
A new irrigation system was installed in this field after the growing season. Managers wonder if the mean weight of pineapples grown in the field this year will be greater than last year. So they take an SRS of 50 pineapples from this year’s crop.
The managers want to perform a test at the α = 0.05 significance level to see if the pineapples this year are heavier.
Confirm that the conditions for conducting a significance test for a mean have been met.

At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces.
A new irrigation system was installed in this field after the growing season. Managers wonder if the mean weight of pineapples grown in the field this year will be greater than last year.  So they take an SRS of 50 pineapples from this year’s crop.

The managers want to perform a test at the α = 0.10 significance level to see if the pineapples this year are heavier.
They found the sample mean weight from this year’s crop was 31.4 ounces and the sample standard deviation was 2.5 ounces.

What is the sample mean? _______ keep all decimal places
What is the mean of the sampling distribution of sample means? _______ 
What is the standard deviation for the sampling distribution of the mean? _______ Round to 3 places past the decimal. See 8.5 for the formula if needed.
Calculate the standardized test statistic (the t statistic) _______ round to 4 places
 .   

At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces.
A new irrigation system was installed in this field after the growing season. Managers wonder if the mean weight of pineapples grown in the field this year will be greater than last year.  So they take an SRS of 50 pineapples from this year’s crop.

The managers want to perform a test at the α = 0.10 significance level to see if the pineapples this year are heavier.
They found the sample mean weight from this year’s crop was 31.4 ounces and the sample standard deviation was 2.5 ounces.

Degrees of freedom = _______  
What degrees of freedom will you use on the t chart? _______ 
Is this a one tailed or a two tailed test? Enter 1 or 2 _______ 
Use the absolute value of the test statistic.
What are the two percentages that correspond to these values? Enter in the same order
 _______   to  _______

Based on the results in the previous question, using an alpha level of 10%, do you have convincing evidence that the pineapples grown this year with the new irrigation system are heavier than last year?

Based on the p value above, what should the conclusion be in this situation?

Identify Type I and Type II Errors in this situation:
Use each answer once.

We think the pineapples are heavier this year and decide to continue using the new irrigation system when the pineapples are actually the same weight, 31 oz, so the new irrigation system did not help.
We think the pineapples are 31 oz and do not use the new irrigation system when it really did help grow heavier pineapples.
We fail to reject the Null Hypothesis by mistake, the Alternative hypothesis is really true
We think the pineapples are 31 oz and do not use the new irrigation system when the pineapples actually are still 31 oz so the irrigation system did not help.
We make the correct decision and reject the Null Hypothesis
We make the correct decision and keep the Null Hypothesis
We reject the Null Hypothesis by mistake, it is really true
We think the pineapples are heavier this year and decide to continue using the new irrigation system when the pineapples are actually heavier showing the system helped.

Type I Error
Type II Error
Not an Error

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. 
Jason chooses an SRS of 60 students and finds that 41 have a computer at home. 
He would like to carry out a test at the α = 0.05 significance level.

Will this be a significance test of a proportion or of a mean.
How do you know?
What parameter are we interested in?

because the problem mentions a mean.

because the problem mentions percent and proportion.

This is a significance test for a mean

This is a significance test for a proportion

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. 
Jason chooses an SRS of 60 students and finds that 41 have a computer at home. 
He would like to carry out a test at the α = 0.05 significance level.

Identify the null and alternative hypothesis.
Define the parameter of interest.

P= the true proportion of students who do not have a computer at home.

U= the trup mean of students who have computers at home.

P= the true proportion of students who have a computer at home.

P= the sample proportion of students who have a computer at home.

At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces. 
A new irrigation system was installed in this field after the growing season. Managers wonder if the mean weight of pineapples grown in the field this year will be greater than last year.  So they take an SRS of 50 pineapples from this year’s crop. 
The managers want to perform a test at the α = 0.10 significance level to see if the pineapples this year are heavier.

P = true mean weight of this year's pineapples

μ = true proportion of this year's pineapples that are heavier than 31 oz

P = true proportion of this year's pineapples that are heavier than 31 oz

μ = true mean weight of this year's pineapples

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school.
Jason chooses an SRS of 60 students and finds that 41 have a computer at home.
He would like to carry out a test at the α = 0.05 significance level.

Confirm that the conditions for conducting a significance test for a mean have been met.

nP > 10, 60(0.68)= 41 >10

Random Sample condition is not met

Large Counts condition is not met, but we will proceed with caution

Per the Central Limit Theorem the shape follows a normal distribution, n >30

"take a random sample of 60 students"

Large Counts condition is met

nP > 10, 60(0.8)= 48 >10

Sample size is large enough, n=60, 60 > 30

Random Sample condition is met

"take an SRS of 60 students"

Normal/Large Sample condition is met

n(1-P) > 10, 60(0.32)= 19 >10

n(1-P) > 10,  60(0.2)= 12 > 10

At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces.
A new irrigation system was installed in this field after the growing season. Managers wonder if the mean weight of pineapples grown in the field this year will be greater than last year.
Will this be a significance test of a proportion or of a mean.
How do you know?
What parameter are we interested in?

because the problem mentions percent and proportion.

because the problem mentions a mean.

This is a significance test for a proportion

This is a significance test for a mean

At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the company’s fields. Last year, the mean weight of the pineapples harvested from one large field was 31 ounces.
A new irrigation system was installed in this field after the growing season. Managers wonder if the mean weight of pineapples grown in the field this year will be greater than last year.  So they take an SRS of 50 pineapples from this year’s crop.
The managers want to perform a test at the α = 0.05 significance level to see if the pineapples this year are heavier.
Confirm that the conditions for conducting a significance test for a mean have been met.

Large Counts condition is met

"take a random sample of 50 pineapples from this year's crop"

Sample size is large enough, n=50, 50 > 30

The sample size is too small (50 < 30)

"take an SRS of 50 pineapples from this year's crop"

Random Sample condition is met

Random Sample condition is not met

Statsmedic.com/applets shows that the distribution is roughly normal.

Per the Central Limit Theorem the shape follows a normal distribution, n >30

Normal/Large Sample condition is not met, but we will proceed with caution

Statsmedic.com/applets does not show that the distribution is roughly normal.

Normal/Large Sample condition is met

Based on the results in the previous question, using an alpha level of 10%, do you have convincing evidence that the pineapples grown this year with the new irrigation system are heavier than last year?

we have convincing evidence that the pineapples grown this year are heavier than last year

the new irrigation system should continue to be used, it showed evidence of an increase in pineapple weight for the entire field

P-value > alpha level

the new irrigation system should not be used, it showed evidence of an increase in pineapple weight just for the sample

we do not have convincing evidence that the pineapples grown this year are heavier than last year

P-value < alpha level

Based on the p value above, what should the conclusion be in this situation?

we have convincing evidence that less than 80% of the students have a computer at home.

0.0122 < 0.05

the P-value < alpha level

Reject the null hypothesis

the P-value > alpha level

we do not have convincing evidence that less than 80% of the students have a computer at home.

0.0122 > 0.05

Fail to reject the null hypothesis

We fail to reject the Null Hypothesis by mistake, the Alternative hypothesis is really true

We think the pineapples are 31 oz and do not use the new irrigation system when the pineapples actually are still 31 oz so the irrigation system did not help.

We make the correct decision and reject the Null Hypothesis

We make the correct decision and keep the Null Hypothesis

We reject the Null Hypothesis by mistake, it is really true

We think the pineapples are heavier this year and decide to continue using the new irrigation system when the pineapples are actually heavier showing the system helped.

Type I Error

Type II Error

Not an Error

JUNIORS ONLY 8.3 & 8.5 Practice Due Mon. 5/13 midnight

JUNIORS ONLY 8.3 & 8.5 Practice Due Mon. 5/13 midnight

Identify Type I and Type II Errors in this situation:Use each answer once.

Based on the results in the previous question, using an alpha level of 10%, do you have convincing evidence that the pineapples grown this year with the new irrigation system are heavier than last year?

Based on the p value above, what should the conclusion be in this situation?

Identify Type I and Type II Errors in this situation:Use each answer once.

Identify Type I and Type II Errors in this situation:
Use each answer once.

Identify Type I and Type II Errors in this situation:
Use each answer once.