5 ### Hypothesis Testing Example#### ContextThe claim is that the weights (in grams) of quarters made after 1964 have a mean equal to 5.670 grams, as required by mint specifications. Given a sample size of \( n = 35 \) and a test statistic of \( t = -2.844 \), find the P-value using statistical software. The task is to determine the final conclusion at a significance level of 0.10.#### Steps for Hypothesis Testing1. **State the Null and Alternative Hypotheses:** - \( H_0: \mu = 5.670 \) - \( H_1: \mu \neq 5.670 \) Here, \( H_0 \) is the null hypothesis stating that the mean weight of quarters is 5.670 grams, and \( H_1 \) is the alternative hypothesis stating that the mean weight is different from 5.670 grams.2. **Test Statistic:** - The test statistic is given as \( t = -2.844 \).3. **Find the P-value:** - Use statistical software to calculate the P-value corresponding to the test statistic of \( -2.844 \).4. **Conclusion:** - Based on the P-value, determine whether there is sufficient evidence to reject the null hypothesis at the 0.10 significance level.#### Analysis- **Interpretation of Results:** Use the calculated P-value to assess if it is less than the significance level of 0.10. If it is, reject the null hypothesis, indicating that there is sufficient evidence to support that the mean weight of quarters differs from 5.670 grams. Otherwise, do not reject the null hypothesis.#### Key Concepts- **Null Hypothesis (\( H_0 \)):** The assumption that there is no effect or no difference.- **Alternative Hypothesis (\( H_1 \)):** The assumption that there is an effect or a difference.- **Test Statistic:** A standardized value used to decide whether to reject the null hypothesis.- **P-value:** The probability of obtaining a result at least as extreme as the observed data, under the assumption that the null hypothesis is true.- **Significance Level (\( \alpha \)):** The threshold for rejecting the null hypothesis; in this case, 0.10.This exercise helps in understanding the process of

Note:- Since you have posted a question with multiple subparts we will provide solutions only to the first three subparts as par our Q&A guidelines. So please repost the remaining subparts separately.5) Given,Claim:- The weights (grams) of quarters made after 1964 have a mean equal to 5.670 g as required by mint specifications.Sample size, n = 35Test statistic, t = -2.844Level of significance, α = 0.10According to the given claim the null and alternative hypotheses are,Test statistic is -2.84 (Rounded to 2 decimal places)Here, degrees of freedom is,df = n-1 = 35-1 = 34Therefore, P-value = 0.007564 (Using Excel function =T.DIST.2T(ABS(-2.84),34) = 0.007564)That is, P-value = 0.008 (Rounded to 3 decimal places)Therefore, hypotheses are, Test statistic is -2.84P-value is 0.008