What are the two decisions that you can make from performing a hypothesis test? What are the two decisions that you can make from performing a hypothesis test? Sele all that apply. \( \begin{array}{ll}\text { A. fail to reject the alternative } \\ \text { hypothesis } & \square \text { B. make a type Il error } \\ \square \text { C. reject the alternative hypothesis } & \square \text { D. fail to reject the null hypothesis } \\ \square \text { E. accept the alternative hypothesis } & \square \text { F. make a type I error } \\ \square \text { G. accept the null hypothesis } & \square \text { H. reject the null hypothesis }\end{array} \)

A restaurant owner is interested in the proportion of his customers who order dessert. He looks at 65 randomly selected receipts. Match the vocabulary word with its corresponding example. - The 65 restaurant patrons whose receipts were observed by the owner - The proportion of the 65 randomly selected customers who ordered dessert answer: Yes or No to whether a customer ordered dessert a. Parameter who come to the restaurant of the 65 Yes or No answers for whether each customer ordered dessert. b. Variable c. Sample d. Population e. Data f. Statistic

4. Un estudio lievado a cabo en cierto distrito escolar dio como resultado que el \( 70 \% \) de los niños de primaria habian mudado de casa por lo menos una ver en su vida. Se saca una muestra aleatoria de 200 niños de este distrito. ¿Cual es la probabilidad de que la proporción de los nif̄os que han mudado de casa por lo menos una vez en su vida esté entre: 0.65 y 0.75 ? y cual es la probabilidad de que la proporción sea mayor que 0.75 ?

wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.002 \). \( H_{o}: \mu=53.1 \) \( H_{a}: \mu \neq 53.1 \) believe the population is normally distributed, but you do not know the standard deviation. You obtain ample of size \( n=15 \) with mean \( M=56.5 \) and a standard deviation of \( S D=5.8 \). at is the \( p \)-value for this sample? (Report answer accurate to four decimal places.)

3.- Un investigador tiene la impresión de que la muestra uno correspondiente al \( 15 \% \), y una muestra dos correspondiente al \( 10 \% \) sufren severamente de pobreza extrema. De la muestra uno compuesta por 150 individuos se encontró que 30 estaban en pobreza extrema y de la muestra dos compuesta por 100 individuos 7 tambièn estaban en pobreza extrema. Suponiendo que esta impresión del investigador es correcta. ¿Cuál es la probabilidad de observar una diferencia entre las proporciones muestrales mayor a igual a la que realmente se observa? (valor \( 10 \% \) )

You wish to test the following claim ( \( H_{a} \) ) at a significance level of \( \alpha=0.002 \). \[ \begin{array}{l}H_{o}: \mu=53.1 \\ H_{a}: \mu \neq 53.1\end{array} \] You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \( n=15 \) with mean \( M=56.5 \) and a standard deviation of \( S D=5.8 \). What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value \( =\square \)