Statistics Questions & Answers

\[ y_{i}=\beta_{1}+\beta_{2} x_{i 2}+\beta_{3} x_{i 3}+\varepsilon_{i}=x_{i}^{\prime} \beta+\varepsilon_{i} \] a. Explain how the ordinary least squares estimator for \( \beta \) is determined and derive an expression for \( b \). b. Which assumptions are needed to make \( b \) an unbiased estimator for \( \beta \) ? c. Explain how a confidence interval for \( \beta_{2} \) can be constructed. Which additional d. Explain how one can test the hypothesis that \( \beta_{3}=1 \).

3.1.5 Data handling consist of a data handling cycle, in which step of the data handling cycle will we identify the mean, mode and median also known as measures of central tendency. Only write the appropriate letter that represents the step. A. Develop a question. B. Collect data. C. Arrange data. D. Summarise data. E. Represent data. F. Analyse data. 3.1 .6 Determine the probability of randomly selecting a month, which has an even number, for the number of niny days in Johannesburg. Write your answer as a fraction.

Assigning lower quotas, the following percentages add up to \( 99 \% \). Using the Hamilton Method, which of them gets its upper quota? \( 13.825 \% \) \( 41.179 \% \) \( 33.471 \% \) \( 12.849 \% \)

Construye una tabla de frecuencias a partir de los siguientes datos de temperatura \( \left({ }^{\circ} \mathrm{C}\right) \) registrados durante 10 dias: \( 22,24,25,22,21,23,22,24,21 \) 23.

As of the 2020 census, the city of Warren, MI has a population of 139,387 . There are 7 city council members. Find the standard divisor. Round to the nearest thousandth, if needed. \( 19,192.286 \) 5.022 \( 19,912.429 \) \( 15,710.857 \)

The Detroit Red Wings' record for the 2021-2022 regular season was \( 32-40-10 \) ( 32 wins, 40 losses, 10 losses in overtime). Determine the percentage of wins. Round to the nearest thousandth of a percent, if needed. \( 48.780 \% \) \( 39.024 \% \) \( 12.195 \% \) \( 32 \% \)

iiendo en cuenta los datos planteados desarrollar los puntos propuestos a continu a. Diagrama de tallo y hoja b. medidas de centralización (media. mediana. moda)

The Detroit Red Wings' record for the 2021-2022 regular season was 32-40-10 ( 32 wins, 40 losses, 10 losses in overtime). Determine the percentage of losses in overtime. Round to the nearest thousandth of a percent, if needed. \( 48.780 \% \) \( 12.195 \% \) \( 39.024 \% \) \( 10 \% \)

As of the 2020 census, the city of Warren, MI has a population of 139,387 . There are 7 city council members. Find the standard divisor. Round to the nearest thousandth, if needed. \( 15,710.857 \) 5.022 \( 19,912.429 \) \( 19,192.286 \)

9.2 In a school, 174 grade 11 learners were interviewed about the social media platforms they are subscribed to and use to share Mathematics tips and lessons. - 37 are on TikTok - 60 are on Instagram - 111 are on YouTube - 29 use TikTok and YouTube - 13 use YouTube and Instagram - 45 are not using any social media platforms and are not subscribed. - \( x \) learners use ALL three social media platforms. (TikTok, Instagram and \( \quad \) YouTube) 9.2.1 \( \quad \) Draw Venn diagram to represent the information above. 9.2.2 Show that \( x=13 \). 9.2.3 Calculate the probability that a learner chosen at random, is subscribed to YouTube and Instagram but not TikTok.