Problem page big corporation advertises that its light bulbs have a mean lifetime, , of at least hours. suppose that we have reason to doubt this claim and decide to do a statistical test of the claim. we choose a random sample of light bulbs manufactured by big and find that the mean lifetime for this sample is hours and that the sample standard deviation of the lifetimes is hours. based on this information, answer the questions below. what are the null hypothesis () and the alternative hypothesis () that should be used for the test? : is : is in the context of this test, what is a type ii error? a type ii error is the hypothesis that is when, in fact, is . suppose that we decide not to reject the null hypothesis. what sort of error might we be making?

Have you ever been in the middle of telling a story and had to use hand gestures or even a drawing to make your point? in algebra, if we want to illustrate or visualize a key feature of a function, sometimes we have to write the function in a different form—such as a table, graph, or equation—to determine the specific key feature we’re looking for. think about interactions with others and situations you’ve come across in your own life. how have you had to adjust or change the way you represented something based on either the concept you were trying to describe or the person you were interacting with? explain how the complexity or layout of the concept required you to change your style or presentation, or how the person’s unique learning style affected the way you presented the information.