Solve the following problems with Minitab. Make sure you write down the hypothes

Question

Solve the following problems with Minitab. Make sure you write down the hypotheses when needed and conclusions to answer the questions. 1) The shelf life of a carbonated beverage is of interest. Ten bottles are randomly selected and tested, and the following results are obtained: Days 108 138 121 163 124 149 126 144 125 139 (a) we would like to show that the median shelf life exceeds 120 days. Set up appropriate hypotheses for investigating this claim. Test these hypotheses using a 0.01. i) State the hypotheses. ii) What is the test statistic? iii) What are the assumptions? iv) What is the p-value for the test? v) What is the decisions? vi) Make Conclusions. 2) The following are the burning times (in minutes) of chemical flares of two differen formulations. The design engineers are interested in both the means and variance of the burning times. 1 Type 2 75 82 73 66 71 67 71 69 57 59 83 84 69 82 68 75 72 71 65 79

Explanation / Answer

since w-ve > w crit, donot reject H0 the median is 120 only

assumptions

distribution must be symmetric. Meaning there shouldn't be outliers

the observations of the sample are independently drawn

z = sum(signed rank)/sqrt(sum(signed rank^2))

-0.25515

x m x-m abs(x-m) rank ( r) signed rank `+ve rank `-ve rank signed rank^2 108 132 -24 24 2 -2 2 4 121 132 -11 11 5 -5 5 25 124 132 -8 8 6 -6 6 36 126 132 -6 6 9.5 -9.5 9.5 90.25 125 132 -7 7 7.5 -7.5 7.5 56.25 138 132 6 6 9.5 9.5 9.5 90.25 163 132 31 31 1 1 1 1 149 132 17 17 3 3 3 9 144 132 12 12 4 4 4 16 139 132 7 7 7.5 7.5 7.5 56.25 132 -5 25 30 384

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