¿Qué supuesto es fundamental para * 1 punto realizar la prueba \( t \) de Student para muestras independientes? \( \begin{array}{l}\text { Las varianzas de ambas muestras deben } \\ \text { ser iguales. }\end{array} \) \( \begin{array}{l}\text { Ambas muestras deben tener el mismo } \\ \text { número de observaciones. }\end{array} \) Los datos deben ser ordinales.

Activity 1 (Measures of Relative Position) Kindly answer this by group, with at most 5 members for each group. Answer this on a whole sheet of paper. 1. Median Income: In 2009 , the median family income in the United States was \( \$ 49,777 \). (Source: U. Census Bureau) If the 90 th percentile for the 2009 four-person family income was \( \$ 137,632 \), find th percentage of families whose 2009 income was a. more than \( \$ 49,777 \). b. more than \( \$ 137,632 \) c. between \( \$ 49,777 \) and \( \$ 137,632 \)

Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January \( 31,2006,9 \) of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that \( 30 \% \) of the stocks traded on the New York Stock Exchange (NYSE) went up the same day. A sample of 76 stocks traded on the NYSE that day showed that 10 went up. You are conducting a study to see if the proportion of stocks that went up is is significantly less than 0.3 . You use a significance level of \( \alpha=\ldots 2 \). What is the test statistic for this sample? Use \( \hat{p} \) rounded to 4 decimal places. (Report answer accurate to 4 decimal places.) test statistic =

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? \( 0.5 \% \) \( 50 \% \) \( 0.25 \% \) \( 25 \% \)

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.