Place your answers on the following answer pages. Show work. Decision Rule: We will reject the Null Hypothesis, H?, if the testing statistic is ___________________ ___________________ 1. Null Hypothesis: H? : ?? – ?? = 0 Alt. Hypothesis: H? : ?? – ?? ___ 0 Pop #1: _________ Pop#2: _________ n? = _________ n? = _________ x?? = _________ x?? = _________ s? = _________ s? = _________ ? = _________ Distribution: t-dist df = n? + n? - 2 = _________ t? = _________ p-value: _________ t.s. = (x?? - x??) – (?? – ??) / s_(x?? - x??) = where s_(x?? - x??) = ?[ ((n? - 1)s?² + (n? - 1)s?²) / (n? + n? - 2) * (1/n? + 1/n?) ] = Result of test : __________________________________________ Final Conclusion: Based on the given information... __________________________________________ __________________________________________ __________________________________________
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Consider the following hypothesis test. $\quad H_{0} : \mu_{1}-\mu_{2}=0$ $H_{\mathrm{a}} : \mu_{1}-\mu_{2} \neq 0$ The following results are from independent samples taken from two populations. a. What is the value of the test statistic? b. What is the value of the degrees of freedom for the $t$ distribution? c. What is the $p$ -value? d. At $\alpha=.05,$ what is your conclusion?
Consider the following hypothesis test. $$ \begin{array}{l} H_{0}: \mu_{1}-\mu_{2}=0 \\ H_{a}: \mu_{1}-\mu_{2} \neq 0 \end{array} $$ The following results are from independent samples taken from two populations. $$ \begin{array}{ll} \text { Sample } 1 & \text { Sample } 2 \\ n_{1}=35 & n_{2}=40 \\ \bar{x}_{1}=13.6 & \bar{x}_{2}=10.1 \\ s_{1}=5.2 & s_{2}=8.5 \end{array} $$ a. What is the value of the test statistic? b. What is the degrees of freedom for the $t$ distribution? c. What is the $p$ -value? d. At $\alpha=.05,$ what is your conclusion?
Consider the following hypothesis test. $$ \begin{array}{l} H_{0}: \mu_{1}-\mu_{2}=0 \\ H_{\mathrm{a}}: \mu_{1}-\mu_{2} \neq 0 \end{array} $$ The following results are for two independent samples taken from the two populations. Sample $1 \quad$ Sample 2 $$ \begin{array}{ll} n_{1}=80 & n_{2}=70 \\ \bar{x}_{1}=104 & \bar{x}_{2}=106 \\ \sigma_{1}=8.4 & \sigma_{2}=7.6 \end{array} $$ a. What is the value of the test statistic? b. What is the $p$ -value? c. With $\alpha=.05,$ what is your hypothesis testing conclusion?
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