Question

one personality test available on the world wide web has a subsection designed to assess the \honesty\ of the test - taker. you are interested in the mean score, μ, among the general population on this subsection. the website reports that μ is 148, but you have good reason to believe that μ is less than 148. you decide to do a statistical test. you choose a random sample of people and have them take the personality test. you find that their mean score on the subsection is 141 and that the standard deviation of their scores is 25. based on this information, complete the parts below. (a) what are the null hypothesis h₀ and the alternative hypothesis h₁ that should be used for the test? h₀:□ h₁:□ (b) suppose that you decide to reject the null hypothesis. what sort of error might you be making? select (c) suppose the true mean score among the general population on the subsection is 148. fill in the blanks to describe a type i error. a type i error would be select the hypothesis that μ is select select when, in fact, μ is select

Explanation:

Step1: Define null and alternative hypotheses

The null hypothesis $H_0$ is the statement of no - effect or the status - quo. The alternative hypothesis $H_1$ is what we suspect to be true. Given that the website reports $\mu = 148$ and we believe $\mu<148$, we have $H_0:\mu = 148$ and $H_1:\mu<148$.

Step2: Identify type of error when rejecting $H_0$

If we reject the null hypothesis $H_0$, we might be making a Type I error. A Type I error occurs when we reject a true null hypothesis.

Step3: Describe Type I error

A Type I error would be rejecting the hypothesis that $\mu$ is equal to 148 when, in fact, $\mu$ is equal to 148.

Answer:

(a) $H_0:\mu = 148$, $H_1:\mu<148$
(b) Type I error
(c) rejecting, equal to 148, equal to 148