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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. \( \quad\left(\begin{array}{cccc}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -2\end{array}\right)\left(\begin{array}{l}\beta_{1} \\ \beta_{2} \\ \beta_{3} \\ \beta_{4}\end{array}\right)=\left(\begin{array}{l}0 \\ 1 \\ 0 \\ 0\end{array}\right) \)

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

6 A sample of people were given two versions of a drink, the original recipe and a new recipe. They were asked, 'Do you prefer the new recipe?" \( 85 \% \) said, yes'. a Why might this result be biased? b How could you arrange the tasting and questioning to avoid bias?

\( \left. \begin{array} { l } { \operatorname { cov } ( x , y ) = \frac { 1 } { 8 } ( 1 \cdot 8 + 3 \cdot 9 + 4 \cdot 12 + 2 \cdot 10 + 5 \cdot 11 } \\ { + 7 \cdot 15 + 8 \cdot 16 + 6 \cdot 13 ) - 4,5 \cdot 11,75 = } \end{array} \right. \)

а) найти числовые характеристики выборки; б) составить эмпирическое уравнение регресси У на X, считау, что данная выборка извлечена из двумерной нормальной совокуп- ности; в) построить корреляционное поле и график эмпирического vдавнения регрессии.

Лабораторна робота № 1 ПЕРВИННА ОБРОБКА ДОСЛІНИХ ДАНИХ - поглибити теоретичні знання з теми: "Первинна обробка дослідних даних"; - прищепити практичні навички аналізу даних, побудови статичного групованого ряду, побудови гістограми та функції розподілу. 3міст роботи: - знайти розмах та об’єм вибірки; - побудувати групований статистичний ряд; - побудувати гістограму вибірки; - побудувати функцію розподілу.