Question

the claim is that weights (grams) of quarters made after 1964 have a mean equal to 5.670 g as required by mint specifications. the sample size is ( n = 38 ) and the test statistic is ( t=-2.766 ). use technology to find the p - value. based on the result, what is the final conclusion? use a significance level of 0.01. state the null and alternative hypotheses. ( h_{0}: mu=5.670 ) ( h_{1}: mu
eq 5.670 ) (type integers or decimals. do not round.) the test statistic is - 2.77 (round to two decimal places as needed.) the p - value is (round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 38\), so \(df=38-1 = 37\)

Step2: Use technology to find the P - value

Since this is a two - tailed test (\(H_1:\mu
eq5.670\)) and the test statistic \(t=-2.766\approx - 2.77\). Using a t - distribution table or statistical software (e.g., TI - 84: tcdf(-1000,-2.77,37)2 or R: 2pt(-2.77,37)), we find the P - value.
The P - value is approximately \(0.008\) (rounded to three decimal places).

Answer:

0.008