Compute the proportion of \( 95 \% \) confidence intervals that fail to circumscribe the true value of \( \mu \) equal to 22.5 grams for \( N=25 \) frogs. Round your answer to four decimal places.

Coffee consumption has been found to be negatively correlated with amount of sleep, with a correlation coefficient of 0.5 . How much can the coffee consumption account for the variance of amount of sleep? \( 0.5 \% \) \( 50 \% \) \( 0.25 \% \) \( 25 \% \)

Which of these values of the correlation coefficient indicates the weakest relationship between two variables? -0.30 -0.18 0.03 0.42

Se obtuvieron los siguientes resultados para el punto de ebullición, en grados Celsius, de un compuesto de silicio: \( \mathbf{1 6 6} \), \( \mathbf{1 4 1 , 1 3 6 , 1 5 3 , 1 7 0 , 1 6 2 , 1 5 5 , 1 4 6 , 1 8 3 ,} \) \( \mathbf{1 5 7 , 1 4 8 , 1 3 2 , 1 6 0 , 1 7 5 y} \mathbf{1 5 0} \). Utilice la prueba de Kolmogorov- Smirnoff con un nivel de significancia de \( \mathbf{0 . 0 1} \) para probar la hipótesis nula de que los puntos de ebullición provienen de una población normal con una media \( \boldsymbol{\mu = 1 6 0}{ }^{\circ} \mathrm{C} \) y una desviación estándar \( \boldsymbol{\sigma = 1 0 ^ { \circ }} \mathrm{C} \)

9 A \( 99 \% \) confidence interval for the mean mass of steel sheets produced in a factory is \( (30.37 \mathrm{~kg}, 32.43 \mathrm{~kg}) \). This interval is based on a random sample of 36 steel sheets. Find a \( 95 \% \) confidence interval for the mean mass of steel sheets, assuming that the masses of steel sheets are normally distributed.

8. For a class project, a political science student at a large university wants to estimate the percent of students who are registered voters. She surveyed 190 students and finds that 80 are registered voters. Compute a \( 98 \% \) confidence interval for the true percent of students who are registered voters and interpret the confidence interval. (Round the answers to 4 decimal places.)