**Research Study on Bacterial Counts in Carpeted vs. Uncarpeted Rooms**A researcher conducted a study to determine if carpeted or uncarpeted rooms contain more bacteria. The table below presents the results for the number of bacteria per cubic foot for both types of rooms. A normal probability plot and boxplot suggest that the data are approximately normally distributed with no outliers. The research aims to answer the question: Do carpeted rooms have more bacteria than uncarpeted rooms at the \(\alpha = 0.01\) level of significance?### Bacterial Data (per cubic foot) for Carpeted and Uncarpeted Rooms| Carpeted | Uncarpeted ||----------|------------|| 12.8 | 6.2 || 9.4 | 10.4 || 9 | 7.8 || 6.4 | 8.7 || 10.4 | 11.9 || 9.3 | 9.5 || 10.8 | 3.3 || 13.6 | 12.3 |### Hypothesis Testing1. **Hypotheses Formulation:** - Null Hypothesis \( H_0 \): \[ \mu_1 = \mu_2 \] - Alternative Hypothesis \( H_1 \): \[ \mu_1 > \mu_2 \]2. **Test Statistic Calculation:** Calculate the test statistic \( t_0 \): \[ t_0 = \]3. **Critical Value Determination:** Use the Student t-distribution table to find the critical value at \(\alpha = 0.01\). Select the correct value and fill in the answer box within your choice: - \[ t_{\alpha/2} = \] - \[ t_\alpha = \]4. **Decision Making:** Do carpeted rooms have more bacteria than uncarpeted rooms at the \(\alpha = 0.01\) level of significance? - A. No, because the test statistic is in the critical region. - B. Yes, because the test statistic is not in the critical region. - C. No, because the test statistic is not in the critical region. -

Carpeted(1) Uncarpeted(2) 12.8 6.2 9.4 10.4 9 7.8 6.4 8.7 10.4 11.9 9.3 9.5…

A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacteria. The table shows the results for the number of bacteria per cubic foot for both types of rooms. A normal probability plot and boxplot indicate that the data are approximately normally distributed with no outliers. Do carpeted rooms have more bacteria than uncarpeted rooms at the a= 0.01 level of significance? Full data setO Uncarpeted 6.2 Carpeted 12.8 9.4 9 9.3 10.4 7.8 6.4 10.4 8.7 11.9 9.5 10.8 13.6 3.3 12.3 E Click the icon to view the Student t-distribution table. What are the null and alternative hypotheses? Student t-distribution Ho: | versus H,: Calculate the test statistic, to- o = (Round to two decimal places as needed.) Now find the critical value. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) Arca in right tal O A. tu/2= -Distribution Area in Right Tail O B. =| Degrees of Freedom 0.25 0.20 015 0.10 0,05 0,025 0.005 0.0025 0.001 0.0005 L000 0816 0.765 0.741 0.727 1963 3.078 1886 1638 1.533 1.476 6.314 2.920 2.353 2.132 2015 12.706 15.894 4.849 3482 2.999 2.757 31821 6.965 4.541 3.747 3.365 63.657 127321 318309 636.619 14.089 2453 5598 4.773 1.376 Do carpeted rooms have more bacteria than uncarpeted rooms at the a=0.01 level of significance? 1.061 1386 4.303 3.182 0.978 1250 0.941 1.190 1156 0.920 9.925 5841 4.604 4.032 22.327 10.215 Z173 31.599 12.924 8610 6869 2.776 2571 O A. No, because the test statistic is in the critical region. O B. Yes, because the test statistic is not in the critical region. OC. No, because the test statistic is not in the critical region. 5893 0.718 0.711 0.706 0.906 0.806 0.889 0883 O870 1134 L119 1108 1100 1.943 1.895 1860 1833 1812 2.447 2365 2.306 2.262 2.228 2.612 2.517 2.449 2.398 2.359 3.143 2.998 2.896 2821 2.764 3.707 1.440 1415 1397 1383 1372 3.499 3.355 3.250 3.169 4317 4.029 3.833 3.690 3.581 5.208 4.785 4.501 4.297 4.144 5.959 5.408 5.041 4.781 4.587 0.703 0.700 10 1093 On Yer hecaure the tert statistic is in the critical region 1407