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.
What is the sample proportion?
What is the mean for the sampling distribution of sample proportions?
What is the standard deviation for the sampling distribution of sample proportions (the standard error)?
What is the standardized test statistic, the z statistic?
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 = 0.10 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?
What is the mean of the sampling distribution of sample means?
What is the standard deviation for the sampling distribution of the mean?
Calculate the standardized test statistic (the t statistic)
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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
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 heavier showing the system helped.
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 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 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 31 oz and do not use the new irrigation system when it really did help grow heavier pineapples.
We make the correct decision and reject the Null Hypothesis
We fail to reject the Null Hypothesis by mistake, the Alternative hypothesis is really true
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.
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.
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.