An LED light bulb manufacturer claims that the average lifespan of its 60-watt LED light bulbs is 43,000 hours. A corporate watchdog group is suspicious of the company's claim and thinks that the true average lifespan of the 60-watt LED light bulbs produced by the company may be less than the advertised 43,000 hours. The group collected and tested a random sample of 240 light bulbs and found the average lifespan of the sample was 42,958 hours. Use the p-value method to test the hypothesis that the mean lifespan of this brand of 60-watt LED light bulb is less than 43,000 hours, using α=0.025α=0.025. Assume the standard deviation of the lifespan of all such light bulbs is known to be 430 hours. State the null and alternative hypothesis for this test. H0:H0: H1:H1: Determine if this test is left-tailed, right-tailed, or two-tailed. right-tailed two-tailed left-tailed Should the standard normal (zz) distribution or Student's (tt) distribution be used for this test? The standard normal (zz) distribution should be used The Student's tt distribution should be used Determine the test statistic for the hypothesis test. Round the solution to two decimal places. Determine the p-value for the hypothesis test. Round the solution to four decimal places. Determine the appropriate conclusion for this hypothesis test. The sample data do not provide sufficient evidence to reject the alternative hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is less than 43,000 hours and thus we conclude that the company's claim that the light bulbs last an average of 43,000 hours is likely false. The sample data provide sufficient evidence to reject the null hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is 43,000 hours and thus we conclude that the company's claim that that the average lifespan of the 60-watt LED light bulbs is 43,000 hours is likely false. The sample data do not provide sufficient evidence to reject the null hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is 43,000 hours and thus we conclude that the company's claim that that the average lifespan of the 60-watt LED light bulbs is 43,000 hours is likely true. The sample data provide sufficient evidence to reject the alternative hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is less than 43,000 hours and thus we conclude that the company's claim that the light bulbs last an average of 43,000 hours is likely true.

An LED light bulb manufacturer claims that the average lifespan of its 60-watt LED light bulbs is 43,000 hours. A corporate watchdog group is suspicious of the company's claim and thinks that the true average lifespan of the 60-watt LED light bulbs produced by the company may be less than the advertised 43,000 hours. The group collected and tested a random sample of 240 light bulbs and found the average lifespan of the sample was 42,958 hours. Use the p-value method to test the hypothesis that the mean lifespan of this brand of 60-watt LED light bulb is less than 43,000 hours, using α=0.025α=0.025. Assume the standard deviation of the lifespan of all such light bulbs is known to be 430 hours. State the null and alternative hypothesis for this test. H0:H0: H1:H1: Determine if this test is left-tailed, right-tailed, or two-tailed. right-tailed two-tailed left-tailed Should the standard normal (zz) distribution or Student's (tt) distribution be used for this test? The standard normal (zz) distribution should be used The Student's tt distribution should be used Determine the test statistic for the hypothesis test. Round the solution to two decimal places. Determine the p-value for the hypothesis test. Round the solution to four decimal places. Determine the appropriate conclusion for this hypothesis test. The sample data do not provide sufficient evidence to reject the alternative hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is less than 43,000 hours and thus we conclude that the company's claim that the light bulbs last an average of 43,000 hours is likely false. The sample data provide sufficient evidence to reject the null hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is 43,000 hours and thus we conclude that the company's claim that that the average lifespan of the 60-watt LED light bulbs is 43,000 hours is likely false. The sample data do not provide sufficient evidence to reject the null hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is 43,000 hours and thus we conclude that the company's claim that that the average lifespan of the 60-watt LED light bulbs is 43,000 hours is likely true. The sample data provide sufficient evidence to reject the alternative hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is less than 43,000 hours and thus we conclude that the company's claim that the light bulbs last an average of 43,000 hours is likely true.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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Related questions

Question

right-tailed
two-tailed
left-tailed

Should the standard normal (zz) distribution or Student's (tt) distribution be used for this test?

The standard normal (zz) distribution should be used
The Student's tt distribution should be used

Determine the test statistic for the hypothesis test. Round the solution to two decimal places.

Determine the p-value for the hypothesis test. Round the solution to four decimal places.

Determine the appropriate conclusion for this hypothesis test.

The sample data do not provide sufficient evidence to reject the alternative hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is less than 43,000 hours and thus we conclude that the company's claim that the light bulbs last an average of 43,000 hours is likely false.
The sample data provide sufficient evidence to reject the null hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is 43,000 hours and thus we conclude that the company's claim that that the average lifespan of the 60-watt LED light bulbs is 43,000 hours is likely false.
The sample data do not provide sufficient evidence to reject the null hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is 43,000 hours and thus we conclude that the company's claim that that the average lifespan of the 60-watt LED light bulbs is 43,000 hours is likely true.
The sample data provide sufficient evidence to reject the alternative hypothesis that the mean lifespan of the 60-watt LED light bulbs produced by this company is less than 43,000 hours and thus we conclude that the company's claim that the light bulbs last an average of 43,000 hours is likely true.

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 + ...

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