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maths statistics

A random sample of students at university was interviewed to
determine the amount of time that they spend on Facebook and
to consider whether the average had changed from its previous level
 
 
 
 
 
 
 
The survey details are:
 
 
 
 
Number of students in the sample (n) =
 
400
 
Average time spent on Facebook (x bar) =
45.4
mins
 
 
 
 
 
 
 
It is known that the standard deviation (s) for the
 
 
amount of time students spend on Facebook =
8
mins
 
 
 
 
 
 
 
In previous years the average amount of time
 
 
spent on Facebook (µ) by students =
 
44
mins
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Write out the null and alternative hypotheses appropriate to 
test whether the average time spent on Facebook has changed.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Carry out the hypothesis test described in Q16a using a
 
95% confidence level (α=0.05).  State your conclusion.
 

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1 Answer

We know for the n=400 sample, x=45.4 and s=8, but we do not know σ, the standard deviation of the population. Therefore, we must use the t-test.
 
H0: µ=44
Ha: µ≠44
Use a calculator to get t=3.5, P=5.18*10-4.
 
Since P<0.05, the result is significant at the 5%-level (even at the 1%-level). Reject the null hypothesis.