Question

Hypothesis Testing: Determining the smallest Significance at which you would be willing to reject the null hypothesis of the following data

Null hypothesis (H_o)
mean =/= 3500
Hypothesis (H_1)
mean = 3500

The range I have determined where we would reject the null hypothesis is:
(3501.5, 3498.5)

Not sure if I'm doing this right, question is below:

i.imgur.com/9d64xhE.png

Answer 1

I got 0.928 for my significance level seems kind of high

Answer 2

This is essentially saying that 92.8% of my given sample size will reject the null hypothesis when it is true. Which is pretty awful.

Answer 3

Are you sure about the \(=/\not=\) designation? Usually the null hypothesis takes on a specific value for the statistic in question, and the alternative says otherwise.

Answer 4

Yes

Answer 5

https://i.imgur.com/nTb6fA6.png

This is the question

Answer 6

Hmm, I'm not convinced that \(\mu=3500\) isn't the null hypothesis.

Consider the test statistic for a \(Z\) test, or maybe a \(T\) test, considering the sample size.
\[Z=\frac{\bar{x}-\mu_0}{\sigma/\sqrt n}~~\text{or}~~T=\frac{\bar{x}-\mu_0}{s/\sqrt n}\]
\(\mu_0\) is an assumed value for the mean, taken from the null hypothesis, so the test statistic would be
\[Z(\text{or }T)=\frac{3450-3500}{60/\sqrt{12}}\]
If the null hypothesis was \(\mu\not=3500\), you wouldn't have a value to use for \(\mu_0\).

Answer 7

Thanks for the help I appreciate it immensely