3. The U.S. Mint has a specification that pennies have a mean weight of 2.5 g. A
ID: 3064386 • Letter: 3
Question
3. The U.S. Mint has a specification that pennies have a mean weight of 2.5 g. A simple random sample of 37 pennies manufactured after 1983 gives a mean weight of 2.499 g and a standard deviation of 0.01648 g. Use confidence interval method to test the claim that the sample is from a population with a mean weight equal to 2.5 g. The significance level is specified as a-0.05. Identify the null hypothesis, alternative hypothesis, test statistic, confidence interval and state your conclusion about the claim.Explanation / Answer
The null and alternate hypothesis is :
Ho: B1 = 2.5
Ha: B1!=2.5
Pop. mean = 2.5g
n = 37
Mean weight of sample = 2.499 h
stdev = .01648 g
alpha = ,05
t statistic = (sample mean - pop. mean)/ (sigma/sqrt(n)) = (2.499-2.5)/(.01648/sqrt(37)) = -.3691
At df = 36 and alpha = .05 the 2 tailed critical t value is .714. The result is not significant at p < .05.
Hence, we conclude that that B1=2.5grams, we do not reject the null hypothesis and conclude that population mean of 2.5 grams.
Condidence interval at 95% confidence
= Pop. mean +/- t*SE
= 2.5 +/- (1.96*.01648/sqrt(37))
= 2.49469 to 2.50531
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