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
(round to two 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: Find the P - value using technology

Since the test is two - tailed (because \(H_1:\mu
eq5.670\)) and \(t=-2.766\), using a t - distribution calculator or software (e.g., in R: 2*pt(-2.766,37)), the P - value is approximately \(0.008\)

Step3: Compare the P - value with the significance level

The significance level \(\alpha = 0.01\). Since \(P - value=0.008<0.01=\alpha\)

Answer:

The P - value is approximately \(0.008\). Since the P - value is less than the significance level of \(0.01\), we reject the null hypothesis \(H_0\). There is sufficient evidence to conclude that the mean weight of quarters made after 1964 is not equal to \(5.670\) grams.