Question

A random sample of 21 nickels in circulation were measured with a very accurate micrometer to find a mean of 0.834343 inch and a standard deviation of 0.001886 inch. At a 5% level of significance, are nickels in circulation on average smaller than the US Mint's manufactured specification of 0.835 inch?

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Answer 1

Here claim is that mean is smaller than 0.835

So hypothesis here is vs

As sample size is less than 30, and population standard deviation is not known, we will use t distribution to find test statistics

The t-critical value for a left-tailed test, for a significance level of α=0.05 is

tc​=−1.725

Graphically

As t statistics do not fall in the rejection region we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that mean is smaller than 0.835