STAT 401    SPRING 2007    HW ARCHIVE

HW1 (tested Sept. 6)
HW1

HW2 ( tested Sept. 13)
Section 7.1 - 3,5(a),(b)
section 7.3 - 32
Use your calculator.
STAT -> TESTS -> TInterval->STATS(enter the sample mean and sample standard deviation)
Section 7.3 - 33(c)
Use your calculator.
STAT->EDIT - enter the data
STAT -> TESTS -> TInterval->Data

HW3 (to be tested Sept. 20)

1. Derive the formulas for the upper and lower-tailed confidence intervals for the mean in a normal distribution when &sigma² is known. (that is the upper and lower-tailed z intervals). Prove that your formulas have the correct confidence levels.


2. Derive the formulas for the upper and lower-tailed confidence intervals for the mean in a normal distribution when &sigma² is unknown (that is the upper and lower-tailed t intervals). Prove that your formulas have the correct confidence levels. Problem section 7.2 - 10 is about confidence intervals related to the parameter &lambda in an exponential distribution. The two-sided case will be covered in class on Tuesday, Feb. 13. Here are two problems about sampling from an exponential distribution.

3. Do Problem 7.2 -10 (a),(b),(c). Use the formula from class for the confidence interval for the reciprocal of the parameter &lambda: in an exponential distribution - this is what the text is trying to derive in Example 7.5.
4. Derive formulas for upper and lower tailed confidence intervals for the parameter &lambda and its reciprocal in an exponential distribution.

HW4 (to be tested Sept. 27)
We first do problems concerning confidence intervals for &sigma and &sigma² in a normal distribution.

1. section 7.4 - 45, 46(b) (43, 44(b) in the fifth edition).
The confidence intervals for sigma and the square of sigma are not available on your calculator. However you can use your calculator to find s and the square of s. Procede as follows
First enter the data
then
STAT -> CALC -> 1VarStats -> s_X.
You will also need the table of chi-squared critical values pg 745 (6-th edition) and page 727 (fifth edition).

Finally we need some problems about the very important case (for real life) of the confidence interval for p in a Bernoulli distribution. We probably won't get this far.
section 7.2 - 19,25
To do 25 use the second (short) formula for n on page 296 (sixth edition) or page 292 (fifth edition). I got 342 for the answer.


HW5 (to be tested Oct.1)
Section 8.1 - 9,12.
Section 8.2 - 18,19,23,29(a),32(a).

Extra Problems
1. Prove that the lower-tailed z-test has significance level α.
2. Prove that the upper-tailed t-test has significance level α.

Minitab assignment   (to be handed in in class Tuesday April 10 )
Download the minitab assigment here minitabassignment
Hand it a printout of your solutions in class. I will not accept solutions via e-mail.

HW6 (to be tested in class October 11)
Derive a formula for β(&mu') for the lower-tailed z-test.
Derive a formula for the P-value of the lower-tailed t-test

Do the following problems on Type II error and sample size for the z-test. Use the formulas on page 320 in Edition 6.
Section 8.2 - 19(b)(c).

Do the following problem on Type II error for the t-test.
Section 8.2 - 29(b). Use the graphs of Table A.17, page 762 in Edition 6.

Do the following problem on Type II error and sample size for the t-test
Section 8.2 - 32(b). Use the graphs of Table A.17, page 762 in Edition 6.

Do the following problem on confidence intervals and tests.
Show that the lower-tailed z-test is equivalent to the decision rule: reject H₀ if μ₀ is not in the lower-tailed confidence interval for μ.

HW7 (to be tested in class October 18)
In the next problem you are to use the formulas concerning the test for a population proportion in Section 8.3. We haven't done this in class. The point is to apply a formula that you haven't seen before. The formulas you need are on page 340 (this gives the decision rule) and page 341 (this gives the formulas for beta and sample size). In all cases the formulas are based on the normal approximation to the binomial.

Section 8.3 - 36(a),(b),(c).
For (a) part use the formulas on page 340. In part (a) ignore the very last question. For part (b) use the formulas for beta on page 341 and for part(c) use the formulas for sample size on page 341.

Problems on P-value
Find a formula for the P-value of the lower-tailed z-test.

HW8 ( On October 25 there will be no homework quiz, just the midterm)
Work the following old Midterm 1
A copy of this midterm in pdf format is available right here: spring06Midterm1 MISSING ASSIGNMENT FOR NOVEMBER 1?

HW9 (Two sample tests: these problems will be tested on Thursday, November 8)


Problems on the two-sample t-tests.
I have described how to Problem 28 below. You will need to decide
TO POOL OR NOT TO POOL First do a preliminary F-test (Section 9.5) on your calculator for the equality of variances. This test is Test #D on your calculator. So test
H₀ : &sigma₁² = &sigma₂²
against
H_a : &sigma₁² &ne &sigma₂²
If you get a high P-value (bigger than .1) than you accept H₀ that the variances are the same and YOU DO A POOLED TEST.
If you get a low P-value (.1 or lower) than you reject H₀ that the variances are the same and YOU DO AN UNPOOLED TEST.
The two-sample t-test is Test #4 on your calculator.
Do the following problems related to the two sample t-test.
Section 9.2 - 21,23(c),25,28.
To do 28 on your calculator load the YF data in L1 and the OF date in L2 and go to TESTS. First do the preliminary F-test to see whether or not you should pool the variances (see above). Then do either the appropriate one-sided pooled t-test or unpooled t-test for the average maximum lean angle. Both the F-test and the t-test operate on the same data (namely the data you have just stored in L1 and L2).



HW10 (these problems will be tested on Thursday, November 15)





TWO PROBLEMS ON THE PAIRED T TEST .
Section 9.3 - 39(b),40
For Problem 39(b) enter the differences (the third line of the tables) in L1 then do a one-sample T test on the entries in L1.
For Problem 40 enter the pipe data in L1 and the brush data in L2. Put the cursor at the very top of L3 (on the name L3). Then enter L1-L2. That will put the differences of the entries in columns L1 and L2 into L3. Now do a one-sample T test on the data in L3.

TWO ANOVA PROBLEMS (these problems are definitely ''good citizen problems")
Section 10.1, Problem 9.
Enter the data in L1,L2,L3,L4.
STAT -> TESTS -> -> F:ANOVA -> ENTER -> ANOVA(L1,L2,L3,L4)-> ENTER
Do Problem 2 from the Fall 2006 Midterm 2. Go to the link below. fall06Midterm2
FIND THE P-VALUE AND COMPARE IT TO ALPHA


HW11 (these problems will be tested on the final on Thursday Nov. )
Make sure you can do the linear regression t-test on your calculator. Do some (or all) of the following questions to get ready for the final.
12.2 #19,20 (a),(b),(c) (save data for 34), 21(b),(c),(d)
12.3 #34(b),37.
Work both of last year's finals before the review on May 17.
Download last fall's final here Stat401finalfall06
Download last springs final here Stat401finalspring06

HW 8 (Midterm 1 is on Thursday, Oct. 26)
Work an old Midterm 1
A copy of this midterm in pdf format is available right here: spring06Midterm1
Work last fall's Midterm 1
A copy of this midterm in pdf format is available right here: fall05Midterm1

HW 9 (tested on Thursday Nov. 16)
This homework assignment was handed out in class.
A copy of this assignment in pdf format is available right here: Stat401HW9

HW 10 (Midterm 2 is on Thursday, Nov. 30)
To get ready for Midterm 2:
1. do the following problems
Section 12.2 # 19,20,21(b),(c),(d),29
Save the data from Problem 20 for Problem 34
Section 12.3 # 34,37 (in both of these problems (β₁)₀ is not equal to zero so you cannot do the test on your calculator).
2. work last spring's Midterm 2.
A copy of this midterm in pdf format is available right here: spring06Midterm2