Inferential Statistics Math Problem - 275 Words

Inferential Statistics (Math Problem Sample) Content: Statistics[Name][Institutional Affiliation]Problem A light bulb manufacturer guarantees that the mean life of a certain light bulb is at least 750 hours. A random Sample of 36 light bulbs has a mean life of 745 hours with a standard deviation of 60 hours.The problem requires that we determine whether at ÃŽ =0.02, we can agree that there is evidence to reject the manufacturerà ¢Ã¢â€š ¬s claim, find the test statistic, the p-value, decide if we can reject the null hypothesis, and interpret the decision in the context of the original claim.CalculationsSteps followed are as follows;From the question presented alongside, the following can be deducted;n=36=750hrsà ¡Ã‚ ª =745hrs à ¢=60Hypothesis testing;In hypothesis testing we present both the null and alternative hypothesis; and prove their worthiness if true or false. Depending on what to test, we accept or accept the null hypothesis as shown below;Claim: H0: The mean half-life of light bulb is at least 750Hrs H1: Th e mean half-life of light bulb is less than 750HrsH0 = à ¢Ã‚ ¥750HrsH1 = 750Hrs This can be tested using a one tailed test in which alpha (ÃŽ=0.02). Hence,To find the statistic; P=, and hence, p=, = -0.5Consider the diagram below;0.02Z= -2.05From the calculation in the z-tables z= -2.05 an... Inferential Statistics Math Problem - 275 Words Inferential Statistics (Math Problem Sample) Content: Statistics[Name][Institutional Affiliation]Problem A light bulb manufacturer guarantees that the mean life of a certain light bulb is at least 750 hours. A random Sample of 36 light bulbs has a mean life of 745 hours with a standard deviation of 60 hours.The problem requires that we determine whether at ÃŽ =0.02, we can agree that there is evidence to reject the manufacturerà ¢Ã¢â€š ¬s claim, find the test statistic, the p-value, decide if we can reject the null hypothesis, and interpret the decision in the context of the original claim.CalculationsSteps followed are as follows;From the question presented alongside, the following can be deducted;n=36=750hrsà ¡Ã‚ ª =745hrs à ¢=60Hypothesis testing;In hypothesis testing we present both the null and alternative hypothesis; and prove their worthiness if true or false. Depending on what to test, we accept or accept the null hypothesis as shown below;Claim: H0: The mean half-life of light bulb is at least 750Hrs H1: Th e mean half-life of light bulb is less than 750HrsH0 = à ¢Ã‚ ¥750HrsH1 = 750Hrs This can be tested using a one tailed test in which alpha (ÃŽ=0.02). Hence,To find the statistic; P=, and hence, p=, = -0.5Consider the diagram below;0.02Z= -2.05From the calculation in the z-tables z= -2.05 an...