So i've recently started brushing up on some areas of maths i'm not farmiliar with and have come across hypotheses testing. Up to this point a friend was helping me out but she's now away until the new year so here i am.

Here's the first of three questions she left me with:

1. A hypothesis test is to be performed to determine whether the mean waiting time during peak hours for bus customers has increased, due to congestion and/or some other factor, from the previous mean waiting time of 8.2 minutes.

Previous experience indicates that the waiting time follows a normal distribution with a standard deviation of 3.8 minutes. To test the hypothesis, a random sample of 25 customers will be selected. This sample of 25 customers yields a mean of 9.75 minutes

- State appropriate null and alternative hypotheses using the standard formal mathematical notation
- Write down what type of test this is. (
two-tailed test,left-tailed test....)- Assuming a significance level of 0.05, whats the critical/rejection region for this test?

dont know why i just cant seem to get on with this topic, if anyone can point me to a good write up/video covering this i'd really appreaciate it.

So far i think my data is:

n = 25

µ = 8.2

x̅ = 9.75

σ = 3.8

first part: (cringe)

H_{o}: σ = 3.8 H_{a}: σ < 3.8

Also is H_{1}the same as H_{a }for the alternate? seen both used in different places.

thanks in advance for any help or guidance.

Jimmy.

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