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.

## maths statistics

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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.

H

_{0}: µ=44H

_{a}: µ≠44Use 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.