A special cable has breaking strength of 756 pounds. The standarddeviation of th

Question

A special cable has breaking strength of 756 pounds. The standarddeviation of the population is 15 pounds. A researcher selects asample of 31 cables and finds that the average breaking strength is751 pounds. Can one reject the claim that the breaking strength is756 pounds? Find the P-value. Should the null hypothesis berejected at = 0.01? Assume that the variable is normallydistributed. Round all intermediate calculations to four decimalplaces.

        A. There is enoughevidence to reject the null hypthosis that the breaking strength is756 pounds.

         B. There is notenough evidence to reject the null hypthosis that the breakingstrength is 756 pounds.

Explanation / Answer

A special cablehas breaking strength of 756 pounds. The standard deviation of thepopulation is 15 pounds. A researcher selects a sample of 31 cablesand finds that the average breaking strength is 751 pounds. Can onereject the claim that the breaking strength is 756 pounds? Find theP-value. Should the null hypothesis be rejected at = 0.01?Assume that the variable is normally distributed. Round allintermediate calculations to four decimalplaces.         A. There is enoughevidence to reject the null hypothesis that the breaking strengthis 756 pounds.     (B) There isnot enough evidence to reject the null hypothesis that thebreaking strength is 756 pounds. {P-Value} =(0.0635) Exceeds (0.01) EXPLANATION: {Null Hypothesis} = {H0: Breaking Strength = 756} {Alt Hypothesis} = {H1: Breaking Strength NOT=756} {Population Mean} = 756 {Population Std Dev} = 15 {Sample Size} = 31 {Sample Mean} = 751 {Std Error Of Mean} = (15)/Sqrt[ (31) ] = 2.694 {Test Value} = ((756) -(751))/(2.694 ) = 1.856 {P-Value} = 1.0 - Prob{-1.856 {Do NOT Reject H0 @0.01} .

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