\( \begin{array}{l} \text { d. } P(Z<z)=0.35 \\ \text { e. } P(Z<z)=0.9772\end{array} \)

The following regression equation is estimated as a production function for Q based on a sample size of 30 observations: \( \ln \left(Q_{i}\right)=1.37+{ }_{0.632}=\ln \left(K_{i}\right)+0.452 \ln \left(L_{i}\right)+\hat{u}_{i} \) \[ R^{2}=0.98 \quad \operatorname{Cov}\left(\hat{\beta}_{\mathrm{K}}, \hat{\beta}_{\mathrm{L}}\right)=0.06 \] and standard errors are in parenthesis, where \( \hat{\beta}_{\mathrm{K}} \) and \( \hat{\beta}_{\mathrm{L}} \) ar capital and labour elsaticities with respect to output, respectively. Test the hypothesis that capital (K) and labour (L) elasticities of output are identical at \( 5 \% \) level of significance 2. Test the hypothesis that there are constant returns to scal at \( 5 \% \) level of significance.

Questão 5 Uma pesquisa foi realizada com 50 estudantes sobre o número de horas que eles dedicam aos estudos por semana. Os dados coletados (em horas) foram os seguintes: \( 5,10,15,10,20,15,25,30,5,10,35,20,15,10,5,25,20,30,35,40,20,25,30,35,40,15,10,25 \), \( 20,30,10,15,20,25,30,35,5,10,15,20,15,20,25,30,35,40,5,10,20,15 \) a) Construa uma tabela de distribuição de frequências com intervalo de classes contendo frequência absoluta, relativa e acumulada. b) Calcule a média, a mediana e a moda.

ABLE 3: QUARTER TWO CRIME STATISTICS IN THE WESTERY CAh FROM 2020 TO 2022. e TABLE 3 above to answer the questions that follow Determine the value of Quartile 2, for the number of crimes commited 2020. 2 If the number of eases for theft from vehicles increased by \( 20,8 \% \) in 2022 Calculate to the nearest hundred, the number of eases from motor vehicle in 2021. 3 Calculate the percentage change in the number of Carjacking between 20 and 2022. You may use the following formula: \[ \text { \%Increase }=\frac{\text { Number of Carjacking in 2022-Number of Carjacking in } 2021}{\text { Number of Carjacking in } 2021} \times 10 \] State, giving a reason, whether the data given in the \% change colum discrete or continuous data.

What is a scatter plot?

12. If \( \sigma=3 \) be the null hypothesis then which one of the following is left sided alternative hypothesis- \( \begin{array}{llll}\text { i) } \sigma+3 & \text { ii) } \sigma<3 & \text { iii) } \sigma>3 & \text { iv) } \sigma=4\end{array} \)