Statistics Questions & Answers

Classify the two given samples as independent or dependent Sample 1: The gas mileage for 48 trucks Sample 2: The gas mileage for 36 cars Choose the correct answer below.

Find the critical value(s) and rejection region(s) for the indicated \( t \)-test, level of significance \( \alpha \), and sample size \( n \). Right-tailed test, \( \alpha=0.05, n=12 \) Click the icon to view the t-distribution table. The critical value(s) is/are (Round to the nearest thousandth as needed, Use a comma to separate answers as needed.)

\( \leftarrow \) A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. \( \mathrm{H}_{0}: \quad \sigma \geq 5.6 \) \( \mathrm{H}_{\mathrm{a}}: \quad \sigma<5.6 \) What type of test is being conducted in this problem? A. Right-tailed test B. Left-tailed test C. Two-tailed test

Test the claim about the difference between two population means \( \mu_{1} \) and \( \mu_{2} \) at the level of significance \( \alpha \). Assume the samples are random and independent, and the populations are normally distributed. Claim: \( \mu_{1} \leq \mu_{2} ; \alpha=0.01 \). Assume \( \sigma_{1}^{2} \neq \sigma_{2}^{2} \) Sample statistics: \( \bar{x}_{1}=2412, s_{1}=174, n_{1}=13 \) and \[ \bar{x}_{2}=2292, s_{2}=55, n_{2}=11 \] Find the standardized test statistic t. \( t=2.35 \) (Round to two decimal places as needed.) Find the P -value. P \( =0.017 \) (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

Sample statistics: \( \bar{x}_{1}=2412, s_{1}=174, n_{1}=13 \) and \[ \mu_{2} \leq 2292, s_{2}=55, n_{2}=11 \] samples are random and independent, and the populations are normally distributed. \[ \begin{array}{ll}H_{a}: \mu_{1}>\mu_{2} & H_{a}: \mu_{1} \geq \mu_{2}\end{array} \] E. \( H_{0}: \mu_{1} \geq \mu_{2} \) \( H_{a}: \mu_{1}<\mu_{2} \)

Test the claim about the difference between two population means \( \mu_{1} \) and \( \mu_{2} \) at the level of significance \( \alpha \). Assume the samples are random and independent, and the populations are normally distributed. Claim: \( \mu_{1} \leq \mu_{2} ; \alpha=0.01 \). Assume \( \sigma_{1}^{2} \neq \sigma_{2}^{2} \) Sample statistics: \( \bar{x}_{1}=2412, s_{1}=174, n_{1}=13 \) and \[ \bar{x}_{2}=2292, s_{2}=55, n_{2}=11 \] \( \begin{array}{ll}\text { A. } H_{0}: \mu_{1}>\mu_{2} & \\ H_{a}: \mu_{1} \leq \mu_{2} & \text { B. } H_{0}: \mu_{1} \neq \mu_{2} \\ \text { C. } H_{0}: \mu_{1} \leq \mu_{2} & H_{a}: \mu_{1}=\mu_{2} \\ H_{a}: \mu_{1}>\mu_{2} & \text { D. } H_{0}: \mu_{1}<\mu_{2} \\ H_{a}: \mu_{1} \geq \mu_{2}\end{array} \) \( \begin{array}{ll}H_{0}: \mu_{1} \geq \mu_{2} & \text { F. } H_{0}: \mu_{1}=\mu_{2} \\ H_{a}: \mu_{1}<\mu_{2} & H_{a}: \mu_{1} \neq \mu_{2}\end{array} \)

Test the claim about the difference between two population means \( \mu_{1} \) and \( \mu_{2} \) at the level of significance \( \alpha \). Assume th samples are random and independent, and the populations are normally distributed. Claim: \( \mu_{1}=\mu_{2} ; \alpha=0.01 \) Population parameters: \( \sigma_{1}=3.3, \sigma_{2}=1.4 \) Sample statistics: \( \bar{x}_{1}=18, n_{1}=28, \bar{x}_{2}=20, n_{2}=30 \) Determine the alternative hypothesis. \( H_{a}: \mu_{1} \square \mu_{2} \) Determine the standardized test statistic. \( z=\square \) (Rousd to two decimal places as needed.) Determine the P-value. P-value = \( \square \) (Round to three decimal places as needed.) What is the proper decision?

Test the claim about the difference between two population means \( \mu_{1} \) and \( \mu_{2} \) at the level of significance \( \alpha \). Assume the samples are random and independent, and the populations are normally distributed. Claim: \( \mu_{1}=\mu_{2} ; \alpha=0.01 \) Population parameters: \( \sigma_{1}=3.3, \sigma_{2}=1.4 \) Sample statistics: \( \bar{x}_{1}=18, n_{1}=28, \overline{x_{2}}=20, n_{2}=30 \) Determine the alternative hypothesis. \( H_{a}: \mu_{1} \square \mu_{2} \)

What conditions are necessary in order to use the \( z \)-test to test the difference between two population proportions? Choose the correct answer below. A. Each sample must be randomly selected, independent, and \( n_{1} p_{1}, n_{1} q_{1}, n_{2} p_{2} \), and \( n_{2} q_{2} \) must be at most five. B. Each sample must be randomly selected, dependent, and \( n_{1} p_{1}, n_{1} q_{1}, n_{2} p_{2} \), and \( n_{2} q_{2} \) must be at most five C. Each sample must be randomly selected, \( I_{\text {dependent, and } n_{1} p_{1}, n_{1} q_{1}, n_{2} p_{2} \text {, and } n_{2} q_{2} \text { must be at least five }}^{\text {D. Each sample must be randomly selected, dependent, and } n_{1} p_{1}, n_{1} q_{1}, n_{2} p_{2} \text {, and } n_{2} q_{2} \text { must be at least five }} \).

What conditions are necessary in order to use the z-test to test the difference between two population proportions? Choose the correct answer below.