Student_Successes

P P P P P P P P P P P P P P P NP P P P NP P P P P P NP P P P P P P P NP P P P P NP P P P P NP P P P P P NP P P P P P P P P P P NP NP P NP P P P NP P P P P P P P NP P P NP P P P P P P P P P P P NP P P P P P P NP P P NP P NP P P P P P P P P P

Part 1: One Proportion Z Confidence Interval The following data represent data gathered from the statistics courses I taught in Spring of 2020 while teaching remotely. P represents pass, and NP represents not pass. Each row is an individual student

Use Excel to create a frequency table to count the number of students who passed (P) in the Excel sheet.

1. Based on your table, the conditions to create a confidence interval for the proportion of my students who pass my statistics classes are met because there are at least 15 NPs and more than 15 Ps.
   • True
   • False
   Assume my students in Spring term of 2020 represent a random sample of my students.
2. What is the point estimate for the proportion of students who pass my class? Round your answer to 3 decimal places properly, and answer as a proportion and not a percent. p=p^= .848
3. What is the margin of error for a 91% confidence interval for the proportion of students who pass my class? Round your answer to 3 decimal places properly, and answer as a proportion and not a percent. me=me= 2.451
4. Choose the best interpretation of the confidence interval you made for proportion of students that pass my class.
   • I am 91% confident that the sample proportion is between 0.791 and 0.905.
   • There is a 91% probability that 84.8% of your students pass.
   • I am 89% confident that between 79.4% and 90.2% of students pass your statistics classes.
   • I am 91% confident that between 0.791 and 0.905 of students pass your statistics classes.

Part 2: One Proportion Z Test In a recent article published by Scientific American found that only 78% of Millennials are certain the world is round. That seems low to you, you believe that more than 78% of Millennials believe the world is round. You randomly sample 86 Millennials and find that 73 of them believe the earth is round. The others didn't necessarily believe it is flat they might just be unsure of the earth's shape.

1. Select the correct answer for null and alternative hypotheses for this test.
   • H0:=0.78H0:=0.78 Ha:0.78Ha:0.78
   • H0:p=0.78H0:p=0.78 Ha:p>0.78Ha:p>0.78
   • H0:=0.78H0:=0.78 Ha:<0.78Ha:<0.78
   • H0:p=0.78H0:p=0.78 Ha:p<0.78Ha:p<0.78
   • H0:p=0.78H0:p=0.78 Ha:p0.78Ha:p0.78
   • H0:=0.78H0:=0.78 Ha:>0.78Ha:>0.7
2. Match each statement with the name of the conclusion for this hypothesis test.
   • -abc When, in reality, the population proportion is greater than 0.78, we conclude that no evidence it is not 0.78. This is a
   • -abc When, in reality, the population proportion is greater than 0.78 we conclude that it is greater than 0.78. This is a
   • -abc When, in reality, the population proportion is 0.78, we conclude the proportion is greater. This is a
   1. Type II error
   2. Type I error
   3. Correct Decision
3. What conditions must be met for you to conduct a Z test for one proportion? (select ALL the correct answers)
   • You are counting the total number of successes in a fixed number of trials.
   • The sample is not known to be random.
   • The sample size is large enough.
   • The claim is about a single mean.
   • The sample is random.
   • The claim is about a single proportion.
   • The population can reasonably be assumed to be normal because sample has approximately a normal distribution.
4. The p-value is (rounded to 4 decimal places)
5. At 0.09 significance level, we conclude that
   • There is enough evidence to claim the proportion of Millennials is truly 78%.
   • There is no enough evidence to support the claim that more than 78% of the population of Millennials believe the world is round. (That is, 78% is a plausible value for the population proportion of Millennials who believe the world is round )
   • There is statistically significant evidence that more than 78% of the population of Millennials believe the world is round.