How do I find the population mean (not the sample mean) in order to solve for t? (Second page) NameIndependent Samples t-test1.The owner of the Shine Company, which manufactures cleaning supplies, suspected that addinga fragrance to a window cleaner leads people to believe that it cleans better than an unscentedproduct. The company selected 24 participants and randomly assigned 12 of them to thescented cleaner and 12 to the unscented cleaner. They had each use it to clean a set ofwindows and then complete a survey on how well the cleaner worked. The survey yielded anumerical value, the "cleaning index," with higher numbers indicating better cleaning.a.State the nondirectional null hypothesis in symbolsHscentedHunscentedorHscented - Hunscented 0b. State the nondirectional alternative hypothesis in symbols.Hscented HunscentedorHscented - Hunscentedc. Using an alpha level of .05 and a two-tailed test, what is the critical value of t?2.069d. Below are the data. Calculate the value of t. I will take you through it step by step.UnscentedScented6499775666679878M = 6SS = 14S= 1.13n = 12M= 7,5SS = 27S= 1.57n= 12First, you must calculate the pooled variance: IF YOUR ANSWER IS 1.86 – CONGRATULATIONS!14+27ニIl +lNow, calculate the estimated standard error: IF YOUR ANSWER IS 0.557 - CONGRATULATIONS!1.861,8631= 0.55670.557%3D1212 Finally, calculate the t value: IF YOUR ANSWER IS 2.69 - CONGRATULATIONS!(6-7,5)-(0,557e. Do you reject the null hypothesis? (Circle one)YESNOf.Based on these data, which of the following is true? (Check one)O windows cleaned with the scented product were rated as cleaner than the windowscleaned with the unscented product.O windows cleaned with the unscented product were rated as cleaner than thewindows cleaned with the scented product.O There was no significant difference in the "cleaning index" between windows cleanedwith the scented product and windows cleaned with the unscented product.g. State your results as if you were writing them for a journal.tLP_.05, two-tailedh. Calculate the effect size using the estimated d. Is this a small, medium, or large effect?IF YOUR ANSWER IS 1.09 - CONGRATULATIONS!i.Now state the directional null hypothesis in symbols.HscentedHunscentedj. State the directional alternative hypothesis in symbols.Hscented Hunscentedk. What is the critical value of t in this case? Assume the alpha level is still.05.Would your conclusion about rejecting the null hypothesis change with a one-tailedtest? Circle one:I.YESNOAdapted from: Steinberg, W.J. (2008). Statistics Alive! Thousand Oaks, CA: Sage.

Hypothesis testing uses data from a sample to draw conclusions about a pop.

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How do I find the population mean (not the sample mean) in order to solve for t? (Second page)

Name
Independent Samples t-test
1.
The owner of the Shine Company, which manufactures cleaning supplies, suspected that adding
a fragrance to a window cleaner leads people to believe that it cleans better than an unscented
product. The company selected 24 participants and randomly assigned 12 of them to the
scented cleaner and 12 to the unscented cleaner. They had each use it to clean a set of
windows and then complete a survey on how well the cleaner worked. The survey yielded a
numerical value, the "cleaning index," with higher numbers indicating better cleaning.
a.
State the nondirectional null hypothesis in symbols
Hscented
Hunscented
or
Hscented - Hunscented 0
b. State the nondirectional alternative hypothesis in symbols.
Hscented Hunscented
or
Hscented - Hunscented
c. Using an alpha level of .05 and a two-tailed test, what is the critical value of t?
2.069
d. Below are the data. Calculate the value of t. I will take you through it step by step.
Unscented
Scented
6
4
9
9
7
7
5
6
6
6
6
7
9
8
7
8
M = 6
SS = 14
S= 1.13
n = 12
M= 7,5
SS = 27
S= 1.57
n= 12
First, you must calculate the pooled variance: IF YOUR ANSWER IS 1.86 – CONGRATULATIONS!
14+27
ニ
Il +l
Now, calculate the estimated standard error: IF YOUR ANSWER IS 0.557 - CONGRATULATIONS!
1.86
1,86
31
= 0.55670.557
%3D
12
12

Finally, calculate the t value: IF YOUR ANSWER IS 2.69 - CONGRATULATIONS!
(6-7,5)-(
0,557
e. Do you reject the null hypothesis? (Circle one)
YES
NO
f.
Based on these data, which of the following is true? (Check one)
O windows cleaned with the scented product were rated as cleaner than the windows
cleaned with the unscented product.
O windows cleaned with the unscented product were rated as cleaner than the
windows cleaned with the scented product.
O There was no significant difference in the "cleaning index" between windows cleaned
with the scented product and windows cleaned with the unscented product.
g. State your results as if you were writing them for a journal.
tL
P_.05, two-tailed
h. Calculate the effect size using the estimated d. Is this a small, medium, or large effect?
IF YOUR ANSWER IS 1.09 - CONGRATULATIONS!
i.
Now state the directional null hypothesis in symbols.
Hscented
Hunscented
j. State the directional alternative hypothesis in symbols.
Hscented Hunscented
k. What is the critical value of t in this case? Assume the alpha level is still.05.
Would your conclusion about rejecting the null hypothesis change with a one-tailed
test? Circle one:
I.
YES
NO
Adapted from: Steinberg, W.J. (2008). Statistics Alive! Thousand Oaks, CA: Sage.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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