The US Mintselects ten pennies from the production line to test the hypothesisth

Question

The US Mintselects ten pennies from the production line to test the hypothesisthat the mean weight of each penny is at least 6 grams. Thenormally-distributed weights (in grams) of these pennies are asfollows: 6, 6, 8, 5, 9, 5, 9, 2, 3, 8. Assumeâ =0.01.
·        State the null and alternatehypotheses
·        Calculate the sample mean andstandard deviation
·        Determine which test statistic isappropriate (z or t), and calculate its value.
·        Determine the criticalvalue(s).
·        State your decision: Should the nullhypothesis be rejected?
The US Mintselects ten pennies from the production line to test the hypothesisthat the mean weight of each penny is at least 6 grams. Thenormally-distributed weights (in grams) of these pennies are asfollows: 6, 6, 8, 5, 9, 5, 9, 2, 3, 8. Assumeâ =0.01.
·        State the null and alternatehypotheses
·        Calculate the sample mean andstandard deviation
·        Determine which test statistic isappropriate (z or t), and calculate its value.
·        Determine the criticalvalue(s).
·        State your decision: Should the nullhypothesis be rejected?

Explanation / Answer

·        State the null and alternatehypotheses Ho: 6 ·        Calculate the sample mean andstandard deviation sample mean is xbar=6.1 standard deviation is s=2.42 ·        Determine which test statistic isappropriate (z or t), and calculate its value. t=(xbar-)/(s/n) =(6.1-6)/(2.42/sqrt(10)) =0.13 ·        Determine the criticalvalue(s). =0.01, t(0.01,df=n-1=9)=2.82 (check student t table) ·        State your decision: Should the nullhypothesis be rejected? Since t=0.13

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