BIG Corporation advertises that its light bulbs have a mean lifetime, μ, of at least 2900 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 2740 hours and that the sample standard deviation of the lifetimes is 750hours. Based on this information, answer the questions below. What are the null hypothesis ( H0 ) and the alternative hypothesis ( H1 ) that should be used for the test? H0 : μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?750 hours2900 hours2740 hours H1 : μ is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?750 hours2900 hours2740 hours In the context of this test, what is a Type I error? A Type I error is ?rejectingfailing to reject the hypothesis that μs ? less than/less than or equal togreater thangreater than or equal tonot equal toequal to ?750 hours2900 hours2740 hours when, in fact, μ is ?less than/less than or equal to greater than greater than or equal tonot equal toequal to ?750 hours2900 hours2740 hours. Suppose that we decide not to reject the null hypothesis. What sort of error might we be making? ?Type IType II

Name: BIG Corporation advertises that its light bulbs have a mean lifetime,
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: BIG Corporation advertises that its light bulbs have a mean lifetime, μ, of at least 2900 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 b

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

Question

BIG Corporation advertises that its light bulbs have a mean lifetime,

μ, of at least 2900 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 2740 hours and that the sample standard deviation of the lifetimes is 750hours.

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 ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?750 hours2900 hours2740 hours

is ?less thanless than or equal togreater thangreater than or equal tonot equal toequal to ?750 hours2900 hours2740 hours

In the context of this test, what is a Type I error?

A Type I error is ?rejectingfailing to reject the hypothesis that

μs ? less than/less than or equal togreater thangreater than or equal tonot equal toequal to ?750 hours2900 hours2740 hours when, in fact, μ is ?less than/less than or equal to greater than greater than or equal tonot equal toequal to ?750 hours2900 hours2740 hours.

Suppose that we decide not to reject the null hypothesis. What sort of error might we be making? ?Type IType II

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions