help with hypotheses testing (wait time for random 25 customers)

[Jimm]

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 H₁ the same as H_a for the alternate? seen both used in different places.


thanks in advance for any help or guidance.

Jimmy.

 

[tkhunny]

Pretty good start. Take a closer read on the problem statement. It asks about the mean waiting time. You defined your hypotheses in terms of the standard deviation, not the mean. Give that another go.