Discussion 5.1 - Assignment Example

Discussion 5 Discussion 5 Example A manufacturer measured the hardness of 25 pieces of an alloy of steel that were sub-critically manufactured, and attained the following data; 167, 163, 179, 187, 167,174, 156,174, 179,159,179, 156,170,174,179,170,156,183,156,187. The manufacturer sets a hypothesis that the mean hardness of all such pieces is greater than 170.Null hypothesis, H0:µ=170Alternative hypothesis, H1::µ> 170 The mean hardness = 172.5 Standard deviation can be evaluated to be 10.31 =2.

06 The Test statistic t t=1.22 The manufacturer sets a significance level = 0, 05 and uses the critical value approach; he would reject the null hypothesis if test statistic is greater than 1.70109 using t table.Since the manufacturers test statistic t = 1.22 is not greater than 1.7109, the operator fails to reject the null hypothesis. Thus the value of the test statistic does not fail in the critical regions.There is insufficient evidence at = 0.05 level to conclude that the average hardness is greater than 170.

Example 2A Phillips bulb manufacturing company claims that a particular model of light bulbs have a lifespan of 850 hours with a standard deviation of 50. A student thinks that the manufactures have overestimated the lifespan of the bulbs 40 hours higher. How many bulbs should the student test to prove his hypothesis with reasonable confidence.Solution We test the lifespan of the light bulbNull hypothesisH0:µ=850H01:µ=810Taking type I error alpha= 0.05The probability that the test rejects the null hypothesis= 0.

90Applying strata sampsi statistical analysis packageSampsi 850 810, SD (50) power (0.9) one sampsiH0: m=850 where m is the population meanAlpha=0.05Power= 0.90H1: m= 810SD=50 The result from the command gives a sample of n=17From the above, it implies that at least 17 light bulbs ought to be tested to reject the null hypothesis under the given hypothesis H1 Example 3A butter manufacturing industry is concerned about the fat content of a certain grade of butter. The manager submits 12 butter samples in the lab for analysis.

The percentage of fat in each of the samples was given as 15,21,19,18,18,14,22,24,19,24,18and 16. The manufacturer claims that the average fat content of this butter should not exceed 20%. Given that the standard deviation is 3.0 use t-hypothesis testing to advice the consumers based on the validity of the industrys claim.SolutionH0: μ = 20%H1: μ < 20% of course 1 tailedSignificance level, α = 0.05 Degrees of freedom, v = n − 1 = 11Critical region, t < −1. 796The average of the 12 samples gives 19.

0The standard deviation= 10.545Test statistic=-1.07The value of the test statistic does not lie in the critical region, therefore, there is no enough evidence to support the manufacturers claim.