Test the claim about the difference between two population means \( \mu_{1} \) and \( \mu_{2} \) at the level of significance \( \alpha \). Assume the samples are random and independent, and the populations are normally distributed. Claim: \( \mu_{1} \leq \mu_{2} ; \alpha=0.01 \). Assume \( \sigma_{1}^{2} \neq \sigma_{2}^{2} \) Sample statistics: \( \bar{x}_{1}=2412, s_{1}=174, n_{1}=13 \) and \[ \bar{x}_{2}=2292, s_{2}=55, n_{2}=11 \] \( \begin{array}{ll}\text { A. } H_{0}: \mu_{1}>\mu_{2} & \\ H_{a}: \mu_{1} \leq \mu_{2} & \text { B. } H_{0}: \mu_{1} \neq \mu_{2} \\ \text { C. } H_{0}: \mu_{1} \leq \mu_{2} & H_{a}: \mu_{1}=\mu_{2} \\ H_{a}: \mu_{1}>\mu_{2} & \text { D. } H_{0}: \mu_{1}<\mu_{2} \\ H_{a}: \mu_{1} \geq \mu_{2}\end{array} \) \( \begin{array}{ll}H_{0}: \mu_{1} \geq \mu_{2} & \text { F. } H_{0}: \mu_{1}=\mu_{2} \\ H_{a}: \mu_{1}<\mu_{2} & H_{a}: \mu_{1} \neq \mu_{2}\end{array} \)

Martina plays chess. She has played 15 games this season, out of which she has won nine. She has five more games to play. What will her success rate be in this season if she wins all five remaining games?

2. En un convivio escolar, se contrató a un taquero que servia tantos tacos como quisiera cada alumno. Cada vez que salía una orden, el mesero anotaba el número de tacos que se pedia: Datos: \( 4,5,2,3,4,3,4,2,3,6,7,3,4,5 \) Se quiere calcular el rango, varianza y desviación estándar de estos datos. Datos: Rango: Varianza:

When is it appropriate to make inferences about a population based upon data collected from a sample when the sample is selected at random from the population of interest any time an experiment is conducted any time an observational study is conducted when a sample is selected from the population of interest

Gallons of milk- \( 24.6,23.84,25.25,21,17.52,19.61,19.83,26.18,34.97 \), \( 29.9,28.59,20.57,26.94,27.24 \) At \( \alpha=0.05 \), test for a significant difference by completing the following. Calculate the value of the test statistic ( 2 decimals). What is the p-value?

According to a recent study annual per capita consumption of milk in the United States is 22.6 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption was entered into the Microsoft Excel Online file below. Use the data to set up your spreadsheet and test your hypothesis. Gallons of milk- \( 24.6,23.84,25.25,21,17.52,19.61,19.83,26.18,34.97 \), \( 29.9,28.59,20.57,26.94,27.24 \) What is a point estimate of the difference between mean annual consumption in Webster City and the national mean?