Seminar Info and Registration 

 

You need to continue studying Lesson 8: Confidence Intervals for the Mean and Lesson 9: Hypothesis Testing for the Mean.  You also need to study Lesson 10: Inferences for Two Means (only in the current edition of Grant's Tutoring Basic Stats 1) and Lesson 11: Inferences about Proportions (formerly Lesson 10 if you have an older edition).

 

Question 1: You will use t to construct the confidence interval for the mean, and test the hypothesis for the mean in this question.  Do you understand why you should use t, instead of z?  Because you are not given σ, the standard deviation of the population.  You are only given s, the sample standard deviation.  Look at my question 14 in Lesson 9 to understand what they are getting at in part (c) and look at question 13 (d) in the same lesson to understand what they are getting at in part (d).

 

Question 2: Very similar to question 1.  Of course, you can use the Stat Mode in your calculator to compute the mean and standard deviation of the given sample.  Look at my question 1 (b) in Lesson 8 for an example of how to interpret a confidence interval for the mean.

 

Question 3:  This is a Matched Pairs problem.  Can you understand why?  Be sure to study Lesson 10 in my new book before you proceed to do this and the next few questions.  Those of you with an older edition of my book will see that I teach Matched Pairs at the end of Lesson 9.

 

This is paired data because each plot is getting both treatments (Sundance and Manitou).  We can only use the matched pairs t method for a sample this small if we can assume the differences for each pair are normally distributed.  Of course, we also need the data to have been collected in a reliable way, using randomization and all other statistical principles to avoid bias.

 

Question 4:  This is clearly a Two-Sample problem (see Lesson 10).  We are given two of everything.  Two sample means, two sample standard deviations, etc.  Do make sure you memorize that the degrees of freedom when using the pooled two-sample t method is n₁ + n₂ - 2 (df = n₁ + n₂ - 2).  Otherwise, the formula sheet you are given in class and on your exam has all the formulas you need to compute the pooled sample variance (s_p²), a confidence interval for the difference between two means, and the test statistic, t, to test the hypothesis that the two means are equal (H₀: μ₁ = μ₂).

 

Think carefully in questions 5, 6 and 7.  They are trying to mix you up.

 

Question 5: This is just a hypothesis test for a mean using t.  Lesson 9 stuff.

 

Question 6: This is a matched pairs t test.  Each university student has two scores, a "social media" score and a "study time" score.  We are only interested in the difference in the scores for each student.  Use the "Difference (Media - Study)" data for the University students.

 

The rest of the assignment uses the formulas taught in Lesson 11 of my book (or Lesson 10 if you have an older edition).  Note that all these formulas are given on the formula sheet you will be supplied on your final exam.

 

Question 8: Use the sample size for proportions formula I teach in my questions 5 and 6.  Again, this formula will be on your formula sheet.  Note that part (c) is using the Inverse-Square Relationship I teach in Lesson 8, question 8.  If you want 1/2 the margin of error, use 4 times the sample size.  You should notice in part (e) that the further p* is from .5, the smaller the sample size you require.  That is why the conservative method sets p* = .5.  You know that no one would ever need a sample size larger than p* = .5 would generate.  But, to save resources, you always take a smaller sample if you can get away with it, that is why we use a value other than .5 for p* if we have a reasonable belief that p* is something other than .5.

 

Question 9: Is a standard confidence interval for the proportion and hypothesis test for the proportion using the formulas I introduce in Lesson 11.  Again, all the required formulas are provided on your formula sheet (except you must memorize that p-hat, the sample proportion, is x/n).

 

Question 10: More of the same.  Look at my Lesson 9, question 6 for examples of interpreting a P-value.