Estadísticas preguntas y respuestas

Para los siguientes planteamientos, calcula el tamaño de muestra que se necesitaria analizar, de acuerdo a la población correspondiente y las condiciones establecidas. a) Se va a realizar un estudio para analizar la cantidad de basura que las per- sonas reciclan en sus casas semanalmente. La población es una escuela con 12.345 integrantes. Se requiere un nivel de confianza del \( 90 \% \) y se estima un error del \( 3 \% \).

a. Mario quiere indagar acerca de la cantidad de tiempo que debe estudiar un alumno del cole- gio en casa. Para ello pregunta a 10 compañeros del curso cuánto tiempo dedica cada uno a estudiar en su casa. b. El dueño de la papelería del barrio quiere saber si es lucrativo implementar el servicio de foto-- copiadora. Para ello preguntó a 57 clientes que ingresaron a la papelería si usarían el servicio y cuántas copias sacarían en una semana.

A newspaper columnist writes that "a majority of Republicans believe that the 2020 election was stolen" What null hypothesis and alternative hypothesis should you use in testing that statement? \( \begin{array}{ll}\mathrm{H}_{0}: p>0.50 & \mathrm{H}_{\mathrm{a}}: p=0.50 \\ \mathrm{H}_{0}: p \neq 0.50 & \mathrm{H}_{\mathrm{a}}: p=0.50 \\ \mathrm{H}_{0}: p=0.50 & \mathrm{H}_{\mathrm{a}}: p>0.50 \\ \mathrm{H}_{0}: p<0.50 & \mathrm{H}_{\mathrm{a}}: p=0.50 \\ \mathrm{H}_{0}: p=0.50 & \mathrm{H}_{\mathrm{a}}: p \geq 0.50 \\ \mathrm{H}_{0}: p=0.50 & \mathrm{H}_{\mathrm{a}}: p \neq 0.50 \\ \mathrm{H}_{0}: p=0.50 & \mathrm{H}_{\mathrm{a}}: p \leq 0.50 \\ \mathrm{H}_{0}: p \neq 0.50 & \mathrm{H}_{\mathrm{a}}: p>0.50\end{array} \)

The mean weight of pills coming off a drug company's manufacturing line is supposed to be 3.7 grams. If a quality control engineer wants to test that the manufacturing line is working property, what null and altemative hypotheses should the engineer use? \( \begin{array}{ll}\mathrm{H}_{0}: \mu=3.7 & \mathrm{H}_{\mathrm{a}}: \mu \geq 3.7 \\ \mathrm{H}_{0}: \mu \neq 3.7 & \mathrm{H}_{\mathrm{a}}: \mu<3.7 \\ \mathrm{H}_{0}: \mu \neq 3.7 & \mathrm{H}_{\mathrm{a}}: \mu=3.7 \\ \mathrm{H}_{0}: \mu \geq 3.7 & \mathrm{H}_{\mathrm{a}}: \mu=3.7 \\ \mathrm{H}_{0}: \mu=3.7 & \mathrm{H}_{\mathrm{a}}: \mu>3.7 \\ \mathrm{H}_{0}: \mu<3.7 & \mathrm{H}_{\mathrm{a}}: \mu-3.7 \\ \mathrm{H}_{0}: \mu=3.7 & \mathrm{H}_{\mathrm{a}}: \mu \neq 3.7 \\ \mathrm{H}_{\mathrm{a}}: \mu=3.7 & \mathrm{H}_{\mathrm{a}}: \mu<3.7\end{array} \)

A college profersor reads a newspaper article that claims that \( 57 \% \) of college students are women. The profersor wonders if that's true. Find the null and alternative hypotheses that would be used to test the statement in the newspaper article. \( \begin{array}{ll}\mathrm{H}_{0}: p=0.57 & \mathrm{H}_{\mathrm{a}}: p \geq 0.57 \\ \mathrm{H}_{0}: p=0.57 & \mathrm{H}_{\mathrm{a}}: p \leq 0.57 \\ \mathrm{H}_{0}: p \neq 0.57 & \mathrm{H}_{\mathrm{a}}: p>0.57 \\ \mathrm{H}_{0}: p>0.57 & \mathrm{H}_{\mathrm{a}}: p=0.57 \\ \mathrm{H}_{0}: p=0.57 & \mathrm{H}_{\mathrm{a}}: p \neq 0.57 \\ \mathrm{H}_{0}: p \neq 0.57 & \mathrm{H}_{\mathrm{a}}: p=0.57 \\ \mathrm{H}_{0}: p<0.57 & \mathrm{H}_{\mathrm{a}}: p=0.57 \\ \mathrm{H}_{0}: p=0.57 & \mathrm{H}_{\mathrm{a}}: p>0.57\end{array} \)

A college professor reads a newspaper article that claims that \( 57 \% \) of college students are women. The professor thinks that the percentage is actually higher than that. Find the null and alternative hypotheses that would be used to test the professor's claim. \( \begin{array}{ll}\mathrm{H}_{0}: \mu=0.57 & \mathrm{H}_{\mathrm{a}}: \mu \neq 0.57 \\ \mathrm{H}_{0}: p \neq 0.57 & \mathrm{H}_{\mathrm{a}}: p=0.57 \\ \mathrm{H}_{0}: p=0.57 & \mathrm{H}_{\mathrm{a}}: p \neq 0.57 \\ \mathrm{H}_{0}: \mu \neq 0.57 & \mathrm{H}_{\mathrm{a}}: \mu=0.57 \\ \mathrm{H}_{0}: p=0.57 & \mathrm{H}_{\mathrm{a}}: p>0.57 \\ \mathrm{H}_{0}: p>0.57 & \mathrm{H}_{\mathrm{a}}: p=0.57 \\ \mathrm{H}_{0}: \mu=0.57 & \mathrm{H}_{\mathrm{a}}: \mu>0.57 \\ \mathrm{H}_{0}: \mu<0.57 & \mathrm{H}_{\mathrm{a}}: \mu=0.57\end{array} \)

A cereal manufacturer claims that the mean weight of cereal in its \( 12-\mathrm{o} \) boxes is at least 12.3 oz. Write the null and alternative hypotheses that would be used to test that claim. \( \mathrm{H}_{0}: \mu=12.3 \quad \mathrm{H}_{\mathrm{a}}: \mu \neq 12.3 \) \( \mathrm{H}_{0}: \mu \neq 12.3 \quad \mathrm{H}_{\mathrm{a}}: \mu=12.3 \) \( \mathrm{H}_{0}: \mu \neq 12.3 \quad \mathrm{H}_{\mathrm{a}}: \mu<12.3 \) \( \mathrm{H}_{0}: \mu=12.3 \quad \mathrm{H}_{\mathrm{a}}: \mu \geq 12.3 \) \( \mathrm{H}_{0}: \mu \geq 12.3 \quad \mathrm{H}_{\mathrm{a}}: \mu=12.3 \) \( \mathrm{H}_{0}: \mu=12.3 \quad \mathrm{H}_{\mathrm{a}}: \mu>12.3 \) \( \mathrm{H}_{0}: \mu=12.3 \quad \mathrm{H}_{\mathrm{a}}: \mu<12.3 \) \( \mathrm{H}_{0}: \mu<12.3 \) \( \mathrm{H}_{\mathrm{a}}: \mu=12.3 \)

\( Q_{A}:(a)- \) Prove that \( \operatorname{cov}\left(y, b_{1}\right)=0 \)

c. La cantidad de horas que un grupo de personas ven TV al día son \( 5,2,1,0,5,4 \), 3,2 y 2 . d. La cantidad de panes que consume un grupo de familias al día en el desayuno son \( 2,4,4,6,5 \) y 6 .

student would like to test that contribution of gender in wage is \( \mathbf{1 \$ 8} \) per hour and that contributi f one year of education is two times greater than one year of experience. What is the appropriate xpression for the joint hypothesis? a. \( \quad\left(\begin{array}{cccc}0 & 1 & 0 & 0 \\ 0 & 0 & -2 & 1\end{array}\right)\left(\begin{array}{l}\beta_{1} \\ \beta_{2} \\ \beta_{3} \\ \beta_{4}\end{array}\right)=\binom{1}{0} \quad \) b. \( \quad\left(\begin{array}{cccc}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -2\end{array}\right)\left(\begin{array}{l}\beta_{1} \\ \beta_{2} \\ \beta_{3} \\ \beta_{4}\end{array}\right)=\left(\begin{array}{l}0 \\ 1 \\ 0 \\ 0\end{array}\right) \)