Problem
ection Question 2, 8.0.0-1 points Part 2 of 4 Points: 0 of 1 The claim is that weights (grams) of quarters made after 1964 have a mean equal to $5.670 \mathrm{~g}$ as required by mi specifications. The sample size is $n=33$ and the test statistic is $t=-3.224$. 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 \[ \begin{array}{l} H_{0} \mu=5.670 \\ H_{1} \mu \neq 5.670 \end{array} \] (Type integers or decimals Do not round) The test statistic is 7 (Round to two decimal places as needed) View an example Get more help - Clear all
Solution
Step 1 ：State the null and alternative hypotheses: \(H_{0}: \mu=5.670\) and \(H_{1}: \mu \neq 5.670\)
Step 2 ：The test statistic is -3.224
Step 3 ：Calculate the degrees of freedom: \(df = n - 1 = 33 - 1 = 32\)
Step 4 ：Find the P-value for a two-tailed t-test with a test statistic of -3.224 and degrees of freedom of 32. The P-value is 0.002907584006793687
Step 5 ：Compare the P-value with the significance level of 0.01. Since the P-value is less than the significance level, we reject the null hypothesis
Step 6 ：The final conclusion is that the mean weight of quarters made after 1964 is not 5.670g. We reject the null hypothesis at a significance level of 0.01. The P-value is \(\boxed{0.0029}\)
