The U.S. Mint has a specification that pennies have a mean weight of 2.5 grams.

Question

The U.S. Mint has a specification that pennies have a mean weight of 2.5 grams. Suppose 30 new pennies made on a certain day were randomly selected and weighed. The average weight of these 30 pennies was 2.5011 grams with a standard deviation of 0.0166 grams. Is there evidence that the population of pennies made on this day do not conform to the specifications? Suppose all conditions are met for performing the one-sample t-test. a. State the ALTERNATIVE hypothesis by filing in the "blanks" in the sentence below. That is, type the correct answer in the squares to correctly state the alternative hypothesis. (Choices for each "blank" are given in parentheses after the square. Choices are separated by a comma Make sure you type the correct answer EXACTLY as it is given in the parentheses.) The (weight, average weight) of (each penny, all pennies, the 30 pennies) made this particular day is (2.5, more than 2.5. less than 2.5, not 2.5, 2.5011) grams. b. The t-statistic for this problem is (round to 2 decimal places after the decimal point) with degrees of freedom (type a value for the degrees of freedom). c. Regardless of your answer to part b, suppose the p-value is 0 005. Type correct answers in the "blanks" to make a correct conclusion based on this p-value. (As in part a. choices are given after each square. Choices are separated by a comma. Make sure you type the correct answer EXACTLY as it is given in the parentheses.) There is (strong, some, not enough) evidence to indicate that pennies made this particular day (conform, do not conform) to the specifications since there is (strong, some, not enough) evidence that the (weight of each penny, average weight of pennies) made this particular day is (less than 2.5, more than 2.5, not 2.5, 2.5, not 2 5011, 2 5011) grams d. A 95% confidence interval for the mean weight of all pennies made this day is to be constructed in the formula below fill in the "blacks" with the correct values. d. A 95% confidence interval for the mean weight of all pennies made this day is to be constructed. In the formula below, fill in the "blanks" with the correct values. The critical value should go in the first set of parentheses after the plusminus and should be rounded to 3 decimal places. All other values should be rounded to 4 decimal places.

Explanation / Answer

Question a)

The average weight of all pennies made this particular day is 2.5 grams.

Question b)

t = ( x bar – Mean) / ( s/ sqrt (n))

   = (2.5011 – 2.5)/(0.0166/sqrt(30))

   = 0.36

Degrees of freedom = n – 1

                                     = 30-1

                                     = 29

The t-statistic for this problem is 0.36 with degrees of freedom 29

Question c)

There is strong evidence to indicate that pennies made this particular day confirm to the specifications since there is strong evidence that the average weight of pennies made this particular day is 2.5 grams.

Question d)

From critical t-table we get the critical tat 5% level of significance for 29 degrees of freedom as 2.045

The value of standard error = s / sqrt (n) = 0.0166 / sqrt (30) = 0.0030

2.5011 (-/+) (2.045) (0.0030)

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