Question

type i error: a company that manufactures steel wires guarantees that the mean breaking strength (in kilonewtons) of the wires is greater than 50. they measure the strengths for a sample of wires and test ( h_0: mu = 50 ) versus ( h_1: mu > 50 ).
part: 0 / 3
part 1 of 3
if a type i error is made, what conclusion will be drawn regarding the mean breaking strength?
the conclusion will be that the mean breaking strength is
select
equal to
not equal to
less than
greater than
less than or greater than
50.

Explanation:

Step1: Recall Type I Error Definition

Type I error is rejecting the null hypothesis ($H_0$) when it is actually true. Here, $H_0: \mu = 50$ and $H_1: \mu > 50$.

Step2: Determine the Conclusion

If we make a Type I error, we incorrectly reject $H_0$ (which says $\mu = 50$) and conclude in favor of $H_1$ (which says $\mu > 50$). But since $H_0$ is true (in the case of Type I error), the conclusion drawn (incorrectly) is that $\mu > 50$. Wait, no—wait, Type I error is rejecting $H_0$ when $H_0$ is true. So the conclusion from the test (due to Type I error) is that we reject $H_0$ (which is $\mu = 50$) and accept $H_1$ (which is $\mu > 50$), but in reality, $\mu = 50$. Wait, no, the question is: "If a Type I error is made, what conclusion will be drawn regarding the mean breaking strength?" So the conclusion drawn (the incorrect one) is that we reject $H_0$ and conclude $H_1$ is true, i.e., $\mu > 50$? Wait, no, wait: Type I error is rejecting $H_0$ when $H_0$ is true. So the conclusion drawn (the error) is that we think $H_1$ is true, so we conclude $\mu > 50$, but actually, $H_0$ is true ($\mu = 50$). Wait, but the question is about the conclusion drawn (not the reality). So the conclusion drawn (due to Type I error) is that we reject $H_0$ (which is $\mu = 50$) and conclude that $\mu > 50$? Wait, no, maybe I got it wrong. Wait, $H_0: \mu = 50$, $H_1: \mu > 50$. Type I error: reject $H_0$ when $H_0$ is true. So the conclusion drawn (the error) is that we conclude $H_1$ is true, so we say $\mu > 50$, but in reality, $\mu = 50$. Wait, but the options are "equal to", "not equal to", "less than", "greater than", "less than or greater than". Wait, no—wait, the null hypothesis is $\mu = 50$, alternative is $\mu > 50$. So when we make a Type I error, we reject $H_0$ (which is true) and conclude $H_1$ is true, so we conclude $\mu > 50$. Wait, but the question is "the conclusion will be that the mean breaking strength is [blank] 50". So the conclusion drawn (the error) is that we think $\mu > 50$, so the conclusion is "greater than" 50? Wait, no, wait: Type I error is rejecting $H_0$ (which is $\mu = 50$) when it's true. So the conclusion drawn (the incorrect one) is that we accept $H_1$, which is $\mu > 50$. So the conclusion is that the mean is greater than 50. Wait, but let's recheck. Type I error: false positive, rejecting $H_0$ when it's true. So the test result says to reject $H_0$ (so we conclude $H_1$), but $H_0$ is actually true. So the conclusion drawn (from the test, due to Type I error) is that $\mu > 50$ (because we rejected $H_0: \mu = 50$ and accepted $H_1: \mu > 50$), even though in reality $\mu = 50$. So the conclusion drawn is "greater than" 50. Wait, but the options are: equal to, not equal to, less than, greater than, less than or greater than. So the correct option is "greater than".

Answer:

greater than