In problems 1-6, fill in the blanks with the appropriate word or words.
1. A____________________is a statement regarding a characteristic of one or more populations.
2. ______________ _____________ is a procedure, based on sample evidence and probability, used to test statements regarding a characteristic of one or more populations.
3. The ____________ ____________ is a statement of no change, no effect, or no difference.
4. The ____________ ____________ is a statement we are trying to find evidence to support.
5. If we reject the null hypothesis when the statement in the null hypothesis is true, we have made a Type _____ error.
6. If we do not reject the null hypothesis when the statement in the alternative hypothesis is true, we have made a Type _____ error.
7. According to the National Association of Home Builders, the mean price of an existing single-family home in 2009 was $218,600. A real estate broker believes that because of the recent credit crunch, the mean price has decreasedsince then.
H0: _____________________
H1: _____________________
This is a LEFT/RIGHT/TWO-TAILED TEST (Circle one)
8. According to the CTIA-The Wireless Association, the mean monthly cell phone bill was $47.47 in 2010. A researcher suspects that the mean monthly cell phone bill is different today.
H0: _____________________
H1: _____________________
This is a LEFT/RIGHT/TWO-TAILED TEST (Circle one)
9. Suppose the mean number of push-ups done in 1 minute by elementary school children as measured in 2010 was 9.8.
However, in the Flenzheim school district this year , a sample of n = 15 students in the 4th grade was taken and the average number of push-ups performed in 1 minute, x--, was 10.1 with a standard deviation, s, of 0.8.
Run a test of hypothesis to determine if the mean number of push-ups done in 1 minute by elementary school children has increased.
Assume the population is normally distributed. Use α = 0.05 as the level of significance.
(1) Set up the null and alternative hypotheses.
H0: _____________________
H1: _____________________
This is a LEFT/RIGHT/TWO-TAILED TEST (Circle one)
(2) Write down the level of significance:α = __________.
(3) Which distribution must I use in running the test? _____________________________
Compute the test statistic:
Compute the p-value:
Find the area to the right of the TEST STATISTIC(if this is a right-tail test; use T.DIST.RT); to the left of the TEST STATISTIC (if this is a left-tail test; use T.DIST); or if this is a two-tail test, use T.DIST.2T).
How many degrees of freedom are there? __________________
What is the p-value? _____________________________________________________
10. Researchers at the University of Mississippi wanted to determine whether the reaction time (in seconds) of males differed from that of females to a go/no go stimulus. The researchers randomly selected 20 females and 15 males to participate in the study. The go/no go stimulus required the student to respond to a particular stimulus and not to respond to other stimuli.
The results are as follows:
|
Female Students
|
Male Students
|
|
0.588
|
0.652
|
0.442
|
0.293
|
0.375
|
0.256
|
0.427
|
|
0.340
|
0.636
|
0.391
|
0.367
|
0.654
|
0.563
|
0.405
|
|
0.377
|
0.646
|
0.403
|
0.377
|
0.374
|
0.465
|
0.402
|
|
0.380
|
0.403
|
0.617
|
0.434
|
0.373
|
0.488
|
0.337
|
|
0.443
|
0.481
|
0.613
|
0.274
|
0.224
|
0.477
|
0.655
|
|
Source: PsychExperiments at the University of Mississippi
|
(1) Set up the null and alternative hypotheses. THIS IS A LEFT / RIGHT / TWO-TAILED TEST(Circle One)
(2) What is the sample evidence?
- The statistics for Females:n1 = _______, x1¯ = ________, and s1 = ________.
- The statistics for Males:n2 = _______, x2¯ = ________, and s2 = ________.
(3) Write down the level of significance α: __________________
(4) Note this is a 2-sample problem. Which distribution must I use in running the test?
(A) USING TECHNOLOGY: THE TI83/84 CALCULATOR
Select the proper test based on your answer to (4) above.
Inpt: (Make sure "Stats" is blinking)
x1-: ____________
Sx1: ___________
n1 = __________
x2-: ___________
Sx2: __________
n2 = _________
(Select one: ≠μ_2<μ_2>μ_2)
Pooled: NO (We assume unequal population variances)
Color (Just arrow down)
Calculate (Just hit "Enter")
What is the p-value? ___________________
Compare: If the p-value <α, REJECT the null hypothesis.
Is the p-value <α? ___________.
(B) MANUAL PROCEDURE
Compute the test statistic: Use the formula in Section 10.1: t-statistic = (x1- - x2- ) / Standard Error, where the Standard Error is given as SQRT (s12/n1 + s22/n2). Note that under the null hypothesis, we take μ1 - μ2 = 0.
What is the test statistic? __________________________________________
Compute the degrees of freedom (df) using the degrees of freedom formula:
df = ((s12/n1 + s22/n2)2 / {[(1/(n1 - 1)(s12/n1)2] + [(1/(n2 - 1)(s22/n2)2 ]}. Round to the nearest integer.
How many degrees of freedom are there? ____________________________
Compute the p-value:
Find the area to the right of the TEST STATISTIC(if this is a right-tail test; use T.DIST.RT); to the left of the TEST STATISTIC (if this is a left-tail test; use T.DIST); or if this is a two-tail test, use T.DIST.2T.
What is the p-value? _____________________________________________
Compare: If the p-value <α, REJECT the null hypothesis.
Is the p-value <α? ___________.