Answered: In October, the campus bookstore asked…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter7: Applying Fractions

Section7.5: Percents

Problem 37WE

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Question

In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. What is an appropriate test value for a z test?

Freshmen
Seniors
Sample size
40
40
Sample mean
$440
$450
Population std. dev.
$57
$68

Expert Solution

Step 1

Hypothesis Testing:

The value of the sample size is more than 30 and the aim is to compare the means of the 2 sample so Z-Test is preferrable.

Two Sample Z-test:

Z score= $\frac{(\bar{x_{1}} - \bar{x_{2}}) - (μ_{1} - μ_{2})}{\sqrt{\frac{σ_{1}^{2}}{n_{1}} + \frac{σ_{2}^{2}}{n_{2}}}}$

where, $\bar{x_{1}}, \bar{x_{2}} a r e t h e s a m p l e m e a n s, μ_{1}, μ_{2} a r e t h e p o p u l a t i o n m e a n s, σ_{1}, σ_{2} a r e t h e P o p u l a t i o n s \tan d a r d d e v i a t i o n s, n_{1}, n_{2} a r e t h e s a m p l e s i z e s .$

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