Haircuts You Need to Find a New Hair Stylist and Know

question 41

Essay

Haircuts You need to find a new hair stylist and know that there are two terrific salons in your area, Hair by Charles and Curl Up & Dye. You want a really good haircut, but you do not want to pay too much for the cut. A random sample of costs for 10 different stylists was taken at each salon (each salon employs over 100 stylists).
a. Indicate what inference procedure you would use to see if there is a significant difference in the costs for haircuts at each salon. Check the appropriate assumptions and conditions and indicate whether you could or could not proceed. (Do not do the actual test.)
b. A friend tells you that he has heard that Curl Up & Dye is the more expensive salon.
i. Write hypotheses for your friend's claim.
ii. The following are computer outputs. Which output is the correct one to use for this test? Explain. $\text { Output A: }$
$\text { Two-sample T' for Hair by Charles vs Curl Up \& Dye }$
$\begin{array}{lrrrr} & \text { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \\\text { Hair by Charles } & 10 & 22.10 & 6.33 & 2.0 \\\text { Curl Up E Dye } & 10 & 26.00 & 4.81 & 1.5\end{array}$

Difference $=$ mu (Hair by Charles) - mu (Curl Up & Dye)
Bstimate for difference: -3.90000
958 CI for difference: ( $-9.22983,1.42983)$
T-Test of difference $=0$ (vs not $=$ ): T-Value $=-1.55 \quad$ P-Value $=0.140$
$\mathrm{DF}=16$

$\text { Output A: }$
$\text { Paired T for Hair by Charlea - Curl Up \& Dye }$
$\begin{array}{lrrrr} & {N} & \text { Mean } & \text { St.Dev } & \text { SB Mean } \\\text { Hair by Charles } & 10 & 22.1000 & 6.3325 & 2.0025 \\\text { Curl Up \& Dye } & 10 & 26.0000 & 4.8074 & 1.5202 \\\text { Difference } & 10 & -3.90000 & 7.37036 & 2.33071\end{array}$

958 CI for mean difference: $(-9.17244,1.37244)$
T-Test of mean difference $=0(\mathrm{vs}$ not $=0): \mathrm{T}$ -Value $=-1.67$ P-Value $=$ 0.129
iii. Use the appropriate computer output to make a conclusion about the hypothesis test based on the data. Make sure to state your conclusion in context.

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Definitions:

Nominal

Referring to data classified into categories without a natural order or ranking among the categories.

Interval Data

A type of data that consists of numerical scores that exist on a scale with equal intervals between values but no true zero point.

Nominal Data

Categorical data that cannot be ordered or ranked in a meaningful way.

Ordinal Data

A type of categorical data with a set order or scale, but without a standard spacing between the categories.