Choose
State the letter / variable we use when we are doing a procedure for means.
(What would you use when you make your hypotheses?)
μ (mew)
Name the 3 conditions for when we use a proportion test.
Random
10%
Large counts
What test statistic are we trying to find when we use proportion tests?
z-score
What causes a Type 1 error?
Actual Truth: Ho True
Decision: Reject the Ho
What value do we use for our test statistics when we conduct a procedure for means?
(Keep in mind statistic - parameter from Tuesday's lesson)
X bar
Name how we would use the Large Counts / Normal condition for a means test
n ≥ 30
Also known as the CLT: If above or equal to 30 our sampling distribution of x bar is approximately normal
How do we calculate our degrees of freedom?
n -1
Our sample size - 1
Draw the 2x2 box that showcases type 1 and 2 errors
See slide 4:
What is our parameter from the following problem. Be specific!
A university claims that the average amount of time students study per week is 15 hours.
A statistics class suspects this is inaccurate, so they randomly sample 40 students and find the average study time.
μ (mew) = The true population mean study time per week (in hours) for all university students
State how you would use the 10% condition for the the following problem:
A small private school has 120 seniors. The administration claims that the average amount of sleep seniors get per night is 7.5 hours. A statistics student believes this is false so they randomly survey 20 seniors to test this claim.
200 ≥ 120 so this condition fails
How do we calculate our p-value when using a t-score?
(What test do you use on your calculator)
tcdf (lower, upper, df)
What conclusion would we make if our p-value is 0.24 and our significance level is 0.05?
We fail to reject the Ho (null hypothesis).
Write a null and alternative hypothesis (WITH UNITS) based on the following information:
A university claims that the average amount of time students study per week is 15 hours.
A statistics class suspects this is inaccurate and the study time is less than 15 hours a week, so they randomly sample 40 students and find the average study time.
Ho: μ (mew) = 15 hours
Ha: μ (mew) < 15 hours
State the significance of all 3 conditions being passed for a means test.
Random: Ensures there is no bias
10%: Ensures our sample is independent, could over/under estimate variability otherwise. Standard error and test statistics assume we have independence.
Normal / Large Counts: Ensures our sample is big enough to have a useful p-value. Keeps the shape of distribution correct.
Calculate the standard deviation with the given information:
Tommy claims that there are exactly 150 chips in his 8 ounce bag of Lays. His friend Timmy went to Costco and bought 45 bags of chips to test this claim. Timmy's mean was 144 chips per bag with a standard deviation of 2.4 chips.
2.4 / square root of 45
= 0.3577
State what full decision you make with the following information:
Ho: μ (mew) = 123.4 feet
Ha: μ (mew) < 123.4 feet
Our p-value is 0.07 and our significance level is 0.05.
Because 0.07 > 0.05 we fail to reject Ho and we do not have convincing evidence that our mean is less than 123.4 feet.
Write the parameter, statistic, null and alternative hypothesis with the following information:
A bottled water company claims that the average amount of water in its bottles is 500 mL.
A consumer group wants to test this claim to see if it is false. They randomly sample 36 bottles and find a mean volume of 492 mL with a standard deviation of 18 mL.
Parameter: the true mean amount of water in all bottles produced by this company
Statistic: x bar = 492 mL
Null: Ho:μ=500 mL
Alternative: Ha:μ≠500 mL or Ha: μ < 500 mL
Test the 3 conditions for the following case. State whether we can keep going through with our test based on the conditions. Show your work!!!
A school counselor believes that students at the school sleep less than 8 hours per night on average.
To investigate, she selects 38 students from a total of 400 students and records their nightly sleep (in hours).
Random: Selected 38 students but not randomly Not passed
10%: 400 students ≥ 380 students Passed
Normal / Large counts: 38 > 30 Passed
We can't continue with our test because we fail the random condition and our sample could have bias.
Calculate a t-score with the following information:
Parameter = 97.8
Statistic: 98.321
Standard deviation from sample: 0.78
n = 34
(statistic - parameter) / (SD / square root of n)
0.521 / 0.133768
= 3.8948
Write a full conclusion based on the following information. Our significance level is 0.10 and our p-value is 0.09. Our null hypothesis is claiming that p = 0.45 and our alternative hypothesis is p > 0.45.
Evidence for Ha: p hat = 0.56 > 0.45
Assuming Ho is true (p = 0.45) there is an 1% probability of getting a p hat of 0.56 or greater purely by chance.
Because 0.09 < 0.10 we reject Ho and we do have convincing evidence that p > 0.45 (our alternative hypothesis).