Answered: 139 trials and found that the mosquito…

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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a certain brand of mosquito repellent claims that it will effectively repel mosquitoes for at least 2 hours. A local biologist thinks that the company’s claim is exaggerated and the length of time for which this brand of mosquito repellent is effect is actually less than 2 hours. to test her hypothesis, the biologist devised a randomized sample of 139 trials and found that the mosquito repellent was effective for 1.97 hours, on average. Use the p-value method to test the hypothesis that the mean effective length of time of this brand mosquito repellent is less than 2 hours , use a significance level of 2% assume the standard deviation of the distribution of all times for which this brand of mosquito repellent is effective is known to be 0.34 hours

Transcribed Image Text:Determine the test statistic for the hypothesis test. O 1.04 O-1.75 O-3.99 O 3.57 Determine the p-value for the hypothesis test. O0.1492 O0.1716 O 0.0659 O0.8508 Determine the appropriate conclusion for this hypothesis test. O The sample data provide sufficient evidence to reject the alternative hypothesis that this brand of mosquito repellent is effective for less than 2 hours on average and thus we conclude that the company's claim that the mosquito repellent is effective for at least 2 hours is likely true. O The sample data do not provide sufficient evidence to reject the alternative hypothesis that this brand of mosquito repellent is effective for less than 2 hours on average and thus we conclude that the company's claim that the mosquito repellent is effective for at least 2 hours is likely false. The sample data provide sufficient evidence to reject the null hypothesis that this brand of mosquito repellent is effective for at least 2 hours and thus we conclude that the company's claim that that the mosquito repellent lasts for at least 2 hours is likely false. O The sample data do not provide sufficient evidence to reject the null hypothesis that this brand of mosquito repellent is effective for at least 2 hours and thus we conclude that the company's claim that that the mosquito repellent lasts for at least 2 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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