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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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