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 )
( h_{1}: mu )
(type integers or decimals. do not round)

Explanation:

Step1: Determine the null and alternative hypotheses

The claim is that the mean is equal to \(5.670\). So, the null hypothesis \(H_0:\mu = 5.670\) and the alternative hypothesis \(H_1:\mu
eq5.670\) (a two - tailed test).

Step2: Calculate the degrees of freedom

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

Step3: Find the P - value using technology

Using a t - distribution calculator (e.g., in R: 2pt(-2.706,37) or in Excel: =2T.DIST(-2.706,37,TRUE)), the P - value is approximately \(0.010\) (rounded to three decimal places)

Step4: Make a conclusion based on the significance level

The significance level \(\alpha = 0.01\). Since the P - value (\(0.010\)) is equal to \(\alpha\), we reject the null hypothesis.

Answer:

• \(H_0:\mu = 5.670\)
• \(H_1:\mu

eq5.670\)

• P - value: approximately \(0.010\)
• Conclusion: Reject \(H_0\). There is sufficient evidence to warrant rejection of the claim that the weights of quarters made after 1964 have a mean equal to \(5.670\) g.