Statistics Questions & Answers

The P-value for a hypothesis test is shown. Use the \( P \)-value to decide whether to reject \( H_{0} \) when the level o significance is (a) \( \alpha=0.01 \), (b) \( \alpha=0.05 \), and (c) \( \alpha=0.10 \). \( P=0.0447 \) (a) Do you reject or fail to reject \( H_{0} \) at the 0.01 level of significance? A. Reject \( H_{0} \) because the \( P \)-value, 0.0447 , is less than \( \alpha=0.01 \). Fail to reject \( H_{0} \) because the \( P \)-value, 0.0447 , is greater than \( \alpha=0.01 \). C. Fail to reject \( H_{0} \) because the \( P \)-value, 0.0447 , is less than \( \alpha=0.01 \). D. Reject \( H_{0} \) because the \( P \)-value, 0.0447 , is greater than \( \alpha=0.01 \) (b) Do you reject or fail to reject \( H_{0} \) at the 0.05 level of significance?

The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject \( \mathrm{H}_{0} \) when the level of significance is (a) \( \alpha=0.01 \), (b) \( \alpha=0.05 \), and (c) \( \alpha=0.10 \). \( \mathrm{P}=0.0447 \) (a) Do you reject or fail to reject \( \mathrm{H}_{0} \) at the 0.01 level of significance? A. Reject \( \mathrm{H}_{0} \) because the P -value, 0.0447 , is less than \( \alpha=0.01 \). Cail to reject \( \mathrm{H}_{0} \) because the P -value, 0.0447 , is greater than \( \alpha=0.01 \). Fail to reject \( \mathrm{H}_{0} \) because the P -value, 0.0447 , is less than \( \alpha=0.01 \). D. Reject \( \mathrm{H}_{0} \) because the \( \mathrm{P}_{\text {-value, }} 0.0447 \), is greater than \( \alpha=0.01 \). (b) Do you reject or fail to reject \( \mathrm{H}_{0} \) at the 0.05 level of significance?

Use the \( t \)-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance \( \alpha \), and sample sizes \( n_{1} \) and \( n_{2} \). Assume that the samples are random and independent, and the populations are normally distributed. Complete parts (a) and (b). \( H_{a}: \mu_{1}>\mu_{2}, \alpha=0.10, n_{1}=6, n_{2}=8 \) Click the icon to view the t-distribution table. (a) Find the critical value(s) assuming that the population variances are equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) (b) Find the critical value(s) assuming that the population variances are not equal. \( \square \)

Use the \( t \)-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance \( \alpha \), and sample sizes \( n_{1} \) and \( n_{2} \). Assume that the samples are random and independent, and the populations are normally distributed. Complete parts (a) and (b) \( H_{a} \mu_{1}>\mu_{2}, \alpha=0.10, n_{1}=6, n_{2}=8 \) Click the icon to view the t-distribution table (a) Find the critical value(s) assuming that the population variances are equal.

Internet provider is trying to gain advertising deals and claims that the mean time the competitors' customers pend online per day is less than 45 minutes. You are asked to test this claim. a) How would you write the null and alternative hypotheses if you represent the Internet provider and want to support he claim? b) How would you write the null and alternative hypotheses if you represent a competing advertiser and want to reject the claim? (a) \( \mathrm{H}_{0}: \) (b) \( \mathrm{H}_{0}: \)

An Internet provider is trying to gain advertising deals and claims that the mean time the competitors' customers spend online per day is less than 45 minutes. You are asked to test this claim. (a) How would you write the null and alternative hypotheses if you represent the Internet provider and want to support the claim? (b) How would you write the null and alternative hypotheses if you represent a competing advertiser and want to reject the claim? (a) \( \mathrm{H}_{0} \)

Use a \( \chi^{2} \)-test to test the claim \( \sigma<44 \) at the \( \alpha=0.05 \) significance level using sample statistics \( s=40.3 \) and \( n=19 \). Assume the population is normally distributed. \( \begin{array}{l}H_{a}: \sigma>44 \\ \text { Identify the standardized test statistic. } \\ 15.10001 \text { (Round to three decimal places as needed.) } \\ \text { Identify the critical value(s). } \\ \square\end{array} \) (Round to three decimal places as needed. Use a comma to separate answers as needed.) Choose the correct conclusion below.

Use a \( \chi^{2} \)-test to test the claim \( \sigma<44 \) at the \( \alpha=0.05 \) significance level using sample statistics \( s=40.3 \) and \( n=1 \). Assume the population is normally distributed. \( H_{0}: \sigma \leq 44 \) Identify the standardized test statistic. 15.10001 (Round to three decimal places as needed.) Identify the critical value(s). \( \square \) (Round to three decimal places as needed. Use a comma to separate answers as needed.) Choose the correct conclusion below.

Use a \( \chi^{2} \)-test to test the claim \( \sigma<44 \) at the \( \alpha=0.05 \) significance level using sample statistics \( s=40.3 \) and \( n=19 \). Assume the population is normally distributed. Identify the null and alternative hypotheses. \( \begin{array}{ll}\text { A. } H_{0}: \sigma>44 & \text { B. } H_{0}: \sigma \geq 44 \\ H_{a}: \sigma \leq 44 & H_{a}: \sigma<44 \\ \text { C. } H_{0}: \sigma \leq 44 & H_{0}: \sigma<44 \\ H_{a}: \sigma>44 & H_{a}: \sigma \geq 44\end{array} \) \( \begin{array}{ll}\text { Identify the standardized test statistic. } & \text { D. } \\ \square \text { (Round to three decimal places as needed.) } & \\ \text { Identify the critical value(s). }\end{array} \)

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. A. The two given samples are independent because different vehicles were sampled. B. The two given samples are dependent because the same vehicles were sampled. C. The two given samples are dependent because different vehicles were sampled. D. The two given samples are independent because the same vehicles were sampled.