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 \[ \bar{x}_{2}=2292, s_{2}=55, n_{2}=11 \] Find the standardized test statistic t. \( t=2.35 \) (Round to two decimal places as needed.) Find the P -value. P \( =0.017 \) (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

standard deviation 3 a normal distribution random variable with mean 23 and that the probability \[ P(X>x)=0.66 \]

When viewing SPSS output, how does one know what decision to make with regard to the \( H_{0} \) ? (A) Ife confidence level lies between the p-value and \( X^{2} \) obt the \( H_{0} \) can be rejected (B) If \( p a \), the \( H_{0} \) can be rejected (C) If the \( x_{0}^{2} \), the \( H_{0} \) is greater be rejected (D) the critical value, the \( H_{0} \) can be retained

A group of researchers are investigating how different studying strategies impact how much participants remember on a test. They recruit 50 participants and have half of the participants study by just reading a passage over and over for 10 minutes. The other half of the participants spend five minutes reading the passage one time and then answering a series of multiple-choice questions on the material for another five minutes. Finally, the participants write down as many facts from the reading passage as they can in three minutes. Which of the following is the dependent variable of the study? (A) Whether they re-read the passage or tested themselves on the material (D) The number of participants in the study

Define un diagrama de dispersión y describe su propósito en la estadística.

In a one-sample t-test, which of the following is true about the null hypothesis? (B) The sample mean is greater than the population mean (C) The sample mean is not equal to the population mean (D) The sample size is larger than 30