Exercise 2

Step 1. Test Set-up

Tony V. owns a house painting business in Seattle. He estimates that it takes his crew three-and-a-half days to paint the interior of a typical house. He has no estimate of the population standard deviation,. He is testing a new paint that is supposed to dry faster than the paint he has been using for over thirty years. He estimates that the average time to paint a house is 3.5 days, the new paint is just as good as the old paint and costs the same. Research Question: Does the new paint allow him to complete a house painting job faster than the paint he has been using? He takes a random sample of 30 homes and paints them with the new paint. Here are the results:

Number of Days to Paint House

The population mean,, is presumed to be 3.5 days and the population standard deviation,, is unknown. Using Microsoft Excel, find the sample mean,X, and sample standard deviation, s, and complete the appropriate significance test.

What test statistic should you use and why?(There are three basic one-sample hypothesis tests: 1) z-test for the population mean, 2) z-test for the population proportion, and 3) t-test for the population mean.)

Based on the research question is this a left-tailed, two-tailed, or right-tailed test?

Step 2. Select the Level of Significance,

A 5 percent significance level has been selected.

What is the Critical Value or Values of the Test Statistic?

Step 3. State the null hypothesis (H₀) and alternate hypothesis (H₁)

H0:
H1:

Follow the examples shown in Clear-Sighted Statistics.You must use the appropriate Greek letters and mathematical symbols.

=			>		<
	2			2	2

Step 4. Compose the decision rule using critical values not p-values. Follow the examples shown in Clear-Sighted Statistics.

Step 5. Calculate the Value of the Test Statistic, p-value, Effect Size, Statistical Power and the Probability of a Type II Error

Step 6: Decide and Report. Your report show cover what your findings mean, whether the test has practical significance, and whether the test has sufficient statistical power or is under or over powered.Do not use the personal pronoun "I" in your report.

Step 6: Decide and Report. Your report show cover what your findings mean, whether the test has practical significance, and whether the test has sufficient statistical power or is under or over powered.Do not use the personal pronoun "I" in your report.

excel data

Significance Level,

0.05

given

3.40

3.75

3.33

3.50

3.33

X-Bar

=AVERAGE(F1:J6)

3.50

3.00

3.40

3.50

3.40

3.500

given

3.00

2.85

3.85

3.33

3.33

s

=STDEV.S(F1:J5)

3.25

3.00

3.50

3.50

3.33

n

Given or =COUNT(F1:J6)

3.33

2.75

3.50

2.75

3.40

df

=B5-1

3.33

3.50

3.50

0.33

3.40

CV of t

#NUM!

=T.INV(B1,B6)

3.50

Given

Decision Rule

Reject the Null Hypothesis if t is < -1.699

Sample Mean

=AVERAGE(F1:J5)

Sampling Error

-3.5000

=B2-B3

Sample Std. Dev.

=STDEV.S(F1:J5)

Standard Error (SEM)

#DIV/0!

=B4/SQRT(B5)

n

=COUNT(F1:J6)

t

#DIV/0!

=B9/B10

p-value

#DIV/0!

=TDIST(ABS(B11),B6,1)

Hypotheses:

H₀:

3.5 days

H₁:

< 3.5 days

Effect Size

#DIV/0!

=ABS(B2-B3)/B4

ES Interpretation

#DIV/0!

=IF(B16>=0.8,"Large",IF(B16>=0.5,"Medium",IF(B16>=0.2,"Small","negligible")))

Effect Size Thresholds

0.2

Small

CV in Units

#NUM!

=B3+(B7*B10)

0.5

Medium

P(Type II)

#NUM!

=T.DIST((B2-B19)/B10,B6,TRUE)

0.8

Large

Power

#NUM!

=1-B20