A ____________________ is a statement regarding a characteristic of one or more populations.

Instructions:

There are 10 problems in this quiz. Problems 1 through 8 are worth 8 points each, for a total of 64 points. Problems 9 and 10, each of which has multiple parts, are worth 18 points each, for a grand total of 100 points.

Build a file to contain your solutions and upload the file per the instructions in the Quiz 3 assignment. YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT.

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.

In Problems 7 and 8 write down the null and alternative hypotheses and identify whether the test would be a left-tail, right-tail, or two-tail test.

  1. 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 decreased since then.

H0: _____________________

H1: _____________________

This is a LEFT/RIGHT/TWO-TAILED TEST (Circle one)

  1. 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)

In problems 9 and 10, you are being asked to run a test of hypothesis. In each problem, you have a choice of using EITHER the TECHNOLOGY (the TI 83/84 calculator) OR the MANUAL PROCEDURE; CHOOSE ONE METHOD or THE OTHER for each problem.

  1. 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? _____________________________

SELECT EITHER (A) TECHNOLOGY (the TI 83/84 calculator) OR (B) the MANUAL PROCEDURE

(A) USING TECHNOLOGY: THE TI 83/84 CALCULATOR

STAT > TESTS

Select the proper test based on your answer to (3) above.

Inpt: (Make sure “Stats” is highlighted)

= _______________

= _______________

= _______________

n = ______________
< > )

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? ___________.

Then we REJECT/ DO NOT REJECT the null hypothesis (circle one).

_____________________________________________________________________.

(B) MANUAL PROCEDURE

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? _____________________________________________________

Compare: If the p-value < α, REJECT the null hypothesis.

Is the p-value < α? ___________.

Then we REJECT/ DO NOT REJECT the null hypothesis (circle one).

  1. 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

Test whether there is a difference in the reaction times of males and females at the α = 0.05 level of significance. ASSUME THE UNDERLYING POPULATIONS ARE NORMAL.

(1) Set up the null and alternative hypotheses. THIS IS A LEFT / RIGHT / TWO-TAILED TEST (Circle One)

H0 : __________________

H1 : __________________

(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? _____________________________

SELECT EITHER (A) TECHNOLOGY (the TI 83/84 calculator) OR (B) the MANUAL PROCEDURE

(A) USING TECHNOLOGY: THE TI83/84 CALCULATOR

Select the proper test based on your answer to (4) above.

Inpt: (Make sure “Stats” is blinking)

Sx1: ___________

n1 = __________

Sx2: __________

n2 = _________

< > )

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? ___________.

Then we REJECT/ DO NOT REJECT the null hypothesis (circle one).

(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 1 – 2 = 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? ___________.

Then we REJECT/ DO NOT REJECT the null hypothesis (circle one).

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