Use technology and a \( t \)-test to test the claim about the population mean \( \mu \) at the given level of significance \( \alpha \) using the given sample statistics. Assume the population is normally distributed. Claim: \( \mu>77 ; \alpha=0.01 \quad \) Sample statistics: \( \bar{x}=79.7, s=2.8, n=27 \) What are the null and altemative hypotheses? Choose the correct answer below. \( \begin{array}{ll}\text { A. } H_{0}: \mu \geq 77 & \text { B. } H_{0}: \mu \neq 77 \\ H_{A}: \mu<77 & H_{A}: \mu=77\end{array} \) \( \begin{aligned} \text { C. } H_{0}: \mu \leq 77 & \text { D. } H_{0}: \mu=77 \\ H_{A}: \mu>77 & H_{A}: \mu \neq 77\end{aligned} \) What is the value of the standardized test statistic?

How do you identify the relationship between two variables in a scatter plot?

Baseball regression line prediction: Suppose the regression line for the number of runs scored in a season, \( y \), is given by \( \hat{y}=-730+4300 x \), where \( x \) is the team's batting average. a. For a tearn with a batting average of 0.235 , find the expected number of runs scored in a season. Round your answer to the nearest whole number. b. If we can expect the number of runs scored in a scason is 480 , then what is the assumed team's batting average? Round your onswer to three deeima! places.

Knowing that \( 99.7 \% \) of all \( z \)-scores are between -3 and +3 , what is the \( P \)-value for \( z=-5.14 \) ? 0.000 0.0514 0.2981

A regression was run to determine if there is a relationship between hours of TV watched per day \( (\mathrm{x}) \) and number of situps a person can do \( (y) \). The results of the regression were: \( \begin{array}{l}\mathrm{y}=\mathrm{ax}+\mathrm{h} \\ \mathrm{a}=2.389 \\ \mathrm{~b}=37.535 \\ \mathrm{r}^{2}=0.412164 \\ \mathrm{r}=-0.642\end{array} \) Use this to predict the number of situps a person who watches 0.5 hours of TV can do (ta one decimal place)

21. Una empresa de investigación de mercado emplea una muestra de individuos para calificar el potencial de compra de un determinado producto antes y después de que los individuos vean un comercial de televisión acerca del mismo. La calificación del potencial de compra se hace con una escala del 0 al 10 , con los valores más altos indicando un mayor potencial de compra. En la hipótesis nula se establece que la media de las calificaciones de "después" será menor o igual a la media de las calificaciones "antes". El rechazo de esta hipótesis indica que el comercial me- jöra la media de la calificación al potencial de compra. Use \( \alpha=0.05 \) y los datos de la tabla si- guiente para probar esta hipótesis y haga un comentario sobre la utilidad del comercial. Calificación al potencial de compra Individuos Después 1