Un gerente de producción desea determinar si existe diferencia entre a productividad de los trabajadores del turno matutino y los de turno vespertino. Para ello, se tomó una muestra aleatoria de 30 trabajadores de cada turno y se encontró que los trabajadores del turno matutino produjeron en promedio 68 artículos en el turno, con una desviación estándar de 16 , en tanto que el turno vespertino produjo en promedio 65.5 articulos, con una desviación estándar de 17 . ¿Existe diferencia entre la productividad de los dos turnos a un nivel de significancia de 0.01 ?

A random sample of 69 produced the summary statistics \( \bar{x}=0.326 \) and \( \mathrm{s}^{2}=0.064 \). Complete parts a and \( b \). a. Test the null hypothesis that \( \mu=0.37 \) against the alternative hypothesis that \( \mu<0.37 \), using \( \alpha=0.10 \). What is the value of the test statistic? \( z=-1.44 \) (Round to two decimal places as needed.) Find the \( p \)-value. p-value \( =\square \) (Round to three decimal places as needed.)

In a normal distribution, a data value located 1.2 standard deviations below the mean has Standard Score: \( \mathrm{z}=\square \)

A variable \( x \) is normally distributed with mean 21 and standard deviation 8 . Round your answers to the nearest hundredth as needed. a) Determine the \( z \)-score for \( x=27 \). \[ z=0.75 \] b) Determine the \( z \)-score for \( x=16 \). \[ z= \]

A random sample of 69 produced the summary statistics \( \bar{x}=0.326 \) and \( s^{2}=0.064 \). Complete parts a and \( b \). State and interpret the results of the test. A. Reject \( H_{0} \). There is insufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \). Bo not reject \( H_{0} \). There is sufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \). C. Reject \( H_{0} \). There is sufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \). Do not reject \( H_{0} \). Thefe is insufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \).

A variable \( x \) is normally distributed with mean 22 and standard deviation 3. Round your answers to the nearest hundredth as needed. a) Determine the \( z \)-score for \( x=27 \). b) Determine the \( z \)-score for \( x=20 \). c) What value of \( x \) has a \( z \)-score of 2.33 ? d) What value of \( x \) has a \( z \)-score of -0.3 ? \( x= \) e) What value of \( x \) has a \( z \)-score of 0 ?