Stat 200 introduction to statistics - how many degrees of

Question

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-: ____________

S_x1: ___________

n₁ = __________

x₂^-: ___________

S_x2: __________

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 = (x_1^- - 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? ___________.