Questions: 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=37 and the test statistic is t=-3.048. Use technology to find the P-value. Based on the result, what is the final conclusion? Use a significance level of 0.10 . State the null and alternative hypotheses. H0: mu = 5.670 H1: mu neq 5.670

Solution Steps

We are testing the claim regarding the mean weight of quarters made after 1964. The null and alternative hypotheses are defined as follows:

\[ \begin{align_} H_0: & \quad \mu = 5.670 \\ H_1: & \quad \mu \neq 5.670 \\ \end{align_} \]

The test statistic provided is \( t = -3.048 \). Using this test statistic, we calculate the p-value for a two-tailed test with \( n = 37 \) (degrees of freedom \( df = n - 1 = 36 \)).

The calculated p-value is:

\[ p\text{-value} \approx 0.0043 \]

We compare the p-value to the significance level \( \alpha = 0.10 \):

\[ p\text{-value} = 0.0043 < \alpha = 0.10 \]

Since the p-value is less than the significance level, we reject the null hypothesis.

Final Answer