Question

2. A college library decides that it will block certain web sites from its computers if they are being used too much of the time on 'recreational' sites (Facebook, games, etc.). The library had decided that they would invest in software to block certain sites if they had statistically significant evidence that the computers were being used for recreation for more than two They'l do a hypothesis test with Ho: (that mean recreational use exceeds 120 minutes per day) is what would cause hours each day H 120 and HA: H>120. Note that the alternative hypothesis action to be taken (purchase of software to block certain sites). 2a) What are the consequences if the test results in a Type I error? Answer in terms of this particular problem, don't just give or paraphrase the definition of a Type I error. (S pns 2b) What are the consequences if the test results in a Type I error? Answer in terms of this particular problem, don't just give or paraphrase the definition of a Type Il error. (S points) For one day they monitor 36 randomly selected computers and record the number of minutes spent on recreational sites. The sample mean was 133 and the standard deviation was 69. a for the mean number of minutes the library's computers are used each Make a 90% confidence day for looking at recreational sites. ter 2c (20 points)

Answer 1

2.

2a)

Consequences of test when test results in type 1 error

Rejected  $H0:\mu=120$ while True mean =$\mu=120$

2b)

Consequences of test when test results in type 2 error

Fail to reject $H0:\mu=120$ while in actual true mean=$\mu>120$

3c)

n=36

sample mean =m =133

sample SD=S=69

so

90% confidence interval is given by

$m \pm Z_{0.05}*\frac{S}{\sqrt{n}}=133 \pm 1.645*\frac{69}{\sqrt{36}}=133 \pm 18.9175$

So interval is given by

(114.0825,151.9175)

2d)

In future, if we find such interval then 90% of times these intervals contain the true mean

2e)

now

120 133 120_110 = 1.130 SİJn 691.736

So P value =P(Z>1.13)=0.13

P value > level of significance (=0.1) Hence we failed to reject H0

2f)

Here we fail to reject the H0 while there is chance that H1 is correct so we can make type 2 error here.