A manufacturer of rechargeable laptop batteries markets its batteries as having, on average, 500 charges. A consumer group decides to test this claim by assessing the number of times 30 of their laptop batteries can be recharged and finds the average is 497, with a standard deviation of 10.The resulting p-value is .1111; thus, the null hypothesis is not rejected. The consumer group concludes that the manufacturer’s claim that its laptop batteries can be recharged, on average, 500 times is accurate.What type of error is possible in this situation?type Itype IIneitherboth
Question
A manufacturer of rechargeable laptop batteries markets its batteries as having, on average, 500 charges. A consumer group decides to test this claim by assessing the number of times 30 of their laptop batteries can be recharged and finds the average is 497, with a standard deviation of 10.The resulting p-value is .1111; thus, the null hypothesis is not rejected. The consumer group concludes that the manufacturer’s claim that its laptop batteries can be recharged, on average, 500 times is accurate.What type of error is possible in this situation?type Itype IIneitherboth
Solution
In this situation, a Type II error is possible. This is because a Type II error occurs when the null hypothesis is not rejected when it is false. In this case, the consumer group did not reject the manufacturer's claim (the null hypothesis), but there could still be a chance that the claim is false, i.e., the actual average number of charges could be different from 500.
Similar Questions
A marketing consulting group wants to see whether placing a seasonal cookie product on an end cap (the shelf at the end of an aisle at a store) will make a difference in sales. The average sales of the seasonal cookie for this region was 650 units. A sample of 36 stores that placed the cookie on an end cap showed a sample mean of 671 units sold with a standard deviation of 81. The resulting p-value is 0.1288; thus, the null hypothesis is not rejected. The marketing consulting group concludes that placing the cookies on an end cap does not affect sales.What type of error is possible in this situation?Group of answer choicesNeitherBothType IType II
A random sample of 15 batteries resulted in an average life of 280 hours with a standard deviation of 24 hours. Assume the battery life to be normally distributed and α = 0.05. Test the following hypothesis:H0: µ = 300 hoursH1: µ ≠ 300 hoursa.reject H0.b.There is no reason to believe that the battery life has changed.c.Accept the null hypothesis.d.Fail to reject the H0.
A 2011 survey by the Bureau of Labor Statistics reported that 91% of Americans have paid leave. In January 2012, a random survey of 1,000 workers showed that 89% had paid leave.The resulting p-value is 0.0271; thus, the null hypothesis is rejected. It is concluded that there has been a decrease in the proportion of people who have paid leave from 2011 to January 2012.What type of error is possible in this situation? Type I Type II Neither Both
A _____ occurs when the sample results lead to not rejecting a null hypothesis that is in fact false.a.Type II errorb.Type III errorc.Type IV errord.Type I errore.power error
In the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:H0 : μ < 8.0 hoursH1 : μ > 8.0 hoursExplain the meaning of a Type II error.Question 2Answera.Concluding that μ > 8.0 hoursb.Failing to reject the hypothesis that μ = 8.0 hours when in fact μ = 8.0 hoursc.Concluding that μ > 8.0 hours when in fact μ > 8.0 hoursd.Failing to reject the hypothesis that μ < 8.0 hours when in fact μ > 8.0 hours
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.