Question

Babcock and Marks (2010) reviewed survey data from 2003–2005 and obtained an average of μ = 14 hours per week spent studying by full-time students at four-year colleges in the United States. To determine whether this average has changed in the past 10 years, a researcher selected a sample of n = 64 of today’s college students and obtained an average of M = 12.5 hours. If the standard deviation for the distribution is σ = 4.8 hours per week, does this sample indicate a significant change in the number of hours spent studying?

Answer 1

Answer:

We do not have enough evidence to accept H₀

Step-by-step explanation:

Normal Distribution

size sample  =  n = 64   (very small sample for evaluating population of 5  years

Standard deviation 4,8

1.- Test hypothesis

H₀             null hypothesis        ⇒               μ₀ = 14       and

Hₐ     alternative hypothesis   ⇒                μ₀ ≠ 14

2.- z(c)  we assume α = 0,05  as we are dealing with a two test tail we should  consider   α/2  = 0.025.

From z table we the z(c) value

z(c) = 1.96           and of course by symmetry   z(c) = -1.96

3.- We proceed to compute z(s)

z(s)  = [ (  μ -  μ₀ ) /( σ/√n) ]           ⇒    z(s)  = - (1.5)*√64/4.8

z(s)  = - 2.5

We compare z(s)  and z(c)

z(s) < z(c)     -2.5  < -1.96  meaning  z(s) is in the rejection zone

we reject H₀ .

From the start we indicate sample size as to small for the experiment nonetheless we found that we dont have enough evidence to accept H₀