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Hypothesis testing with the normal distribution

when doing these types of questions,I always get the value of μ and the value of X bar mixed up, can someone please tell me how to figure out which is which
Reply 1
Original post by Noname60
when doing these types of questions,I always get the value of μ and the value of X bar mixed up, can someone please tell me how to figure out which is which

Screenshot 2024-04-25 134900.png
Reply 2
Original post by Noname60
Screenshot 2024-04-25 134900.png

In a sense it doesnt really matter as youre calculating the difference (two tailed, so sign doesnt matter), but it would be better to say (test whether) the sample mean is a normal random variable with mean equal to the population mean and the variance equal to the population variance/n so
xbar ~ N(mu, sigma^2/n)
so here xbar = 8.95 (the mean of the sample), and the population parameters are mu=9, sigma^2=0.15^2, and n=30
(edited 2 months ago)
Reply 3
Original post by mqb2766
In a sense it doesnt really matter as youre calculating the difference (two tailed, so sign doesnt matter), but it would be better to say (test whether) the sample mean is a normal random variable with mean equal to the population mean and the variance equal to the population variance/n so
xbar ~ N(mu, sigma^2/n)
so here xbar = 8.95 (the mean of the sample), and the population parameters are mu=9, sigma^2=0.15^2, and n=30

oh thank you very much for your help, I get it now🙂

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