Null hypthesis?

Question

A manufacturer has developed a new kind of mobile-phone battery that he claims has a mean lifetime of 8.0 hours with a standard deviation of 0.5 hour. To test the null hypothesis that µ =8.0 hours versus the alternatives that µ <8.0 hours, a random sample of 50 batteries will be tested. The critical region is defined to be x < 7.9, ie. Reject the null hypothesis if sample mean is found to be less than 7.9 hours. Find the probabilities of committing (i) a type I error; (ii) a type II error when µ=7 hours

Answer 1

To answer this question, you need a standard deviation for the lifetimes of the batteries.

The question is asking you to determine the area on the bell curve below the value x =7.9, if the bell curve has a mean of 8. But, to determine the area under a region of a bell curve, you must know the bell curve's mean and standard deviation.

Was any further info given in the question?

Answer 2

on account which you could't tutor something in technological know-how, what you consistently might use is the null hypothesis, the place you the two say there is not any correlation between what you're sorting out (accepting the null hypothesis), or you're saying that there is an significant correlation between the two variables (reject the null hypothesis). yet whilst there is already pre-latest examine that backs up your theory, or in case you pick for to retest their hypothesis, then you definately might use a commerce hypothesis or experimental hypothesis, the place you will possibly state that there is a correlation between blah and blah. yet regularly you're greater probable to apply the null hypothesis, because it extremely is the sole hypothesis the place you need to use a statistical attempt to objective if the correlation is substantial, e.g. chi squared, spearman's rank.

Answer 3

In spite of what someone else said, you do have a standard deviation here.

With 50 in your sample, you would most likely do a z-test for this problem.

z = (xbar - mu)/(SD / SQR(n))

You'll then use your tables to find the probabilities associated with that z-score.