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# Finding Type 1 Probability? watch

1. I've been struggling with this question for over two hours today, all the examples on the net seem irrelevant to my actual question. And I have 15 to do! Here is the first one:

A manufacturer has developed a fishing line that is claimed to have a mean breaking strength of 10kg with a known standard deviation of 0.6kg. Suppose that the breaking strength follows a normal distribution. With a sample size of n=50, the null hypothesis that mu=10kg, against the alternative hypothesis that mu<10kg, will be rejected if the sample mean x(bar)<9.75kg.

Find the probability of committing a type 1 error.

I don't even know what to search for apart from 'find probability of committing a type 1 error' in which case I get loads of irrelevant search results. Please help me!
2. (Original post by epsilondelta)
I've been struggling with this question for over two hours today, all the examples on the net seem irrelevant to my actual question. And I have 15 to do! Here is the first one:

A manufacturer has developed a fishing line that is claimed to have a mean breaking strength of 10kg with a known standard deviation of 0.6kg. Suppose that the breaking strength follows a normal distribution. With a sample size of n=50, the null hypothesis that mu=10kg, against the alternative hypothesis that mu<10kg, will be rejected if the sample mean x(bar)<9.75kg.

Find the probability of committing a type 1 error.

I don't even know what to search for apart from 'find probability of committing a type 1 error' in which case I get loads of irrelevant search results. Please help me!
A type 1 error in hypothesis testing means (I think) rejecting the null hypothesis when it is actually true. In this case, it looks as though the probability of committing a type 1 error will be equivalent to the probability of a sample of size n = 50 having a sample mean of <9.75 when the population mean is actually 10.

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Updated: March 5, 2018
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