Consider the discrete random variable X1, with probability pi X = with probability p2 X2, with probability p3 where x1=-2.3, X2=0, X3=2.3, p1=0.23, X3, P2=0.28. Find the variance of the random variable Y = X2.

Two separate samples, each with n = 14 individuals, receive different treatments. After treatment, the first sample has SS = 1316 and the second has SS = 1620. Find the pooled Variance for two independent samples. (hundredths place) Type only the pooled variance.

Let x be a random variable that represents the pH of CVS brand water. The mean of this x distribution is µ = 6.5 pH. A new company wants to sell its water at CVS locations. However, CVS management believes that the new brand will have a mean pH less than the CVS brand water. A random sample of 50 water samples were taken from this new company's water and it was found that the sample mean was 6.3 pH and the sample standard deviation was s = 0.5 pH. Do the data indicate that the new company's water has a mean pH level less than 6.5, which is the pH of the CVS brand water. Use a 5% significance level. Identify the following in your answer. 1. Identify the null Ho and alternative hypotheses H1 for the problem. 2. Identify the following: Sample statistic • Test Statistic (t): (Round to three decimal places) p - value: (Round to four places) • Calculator key used. 3. Identify the significance level and determine if you reject or fail to reject the null hypothesis. 4. State your conclusion.

A researcher takes sample temperatures in Fahrenheit of 16 days from Miami and 14 days from Atlanta. Use the sample data shown in the table. Test the claim that the mean temperature in Miami greater than the mean temperature in Atlanta. Use a significance level of α=0.10α=0.10.Assume the populations are approximately normally distributed with unequal variances.Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs.   Miami Atlanta 68.3 73.6 83.1 69.3 79.1 54.9 72 81.1 72.8 78.6 83.3 54 82.7 36.1 80.7 44.3 87 58.4 83.1 50.8 77.4 60.5 86.1 61.2 76.3 46.8 74.5 54.4 83.3   78.5     The Null Hypotheses is: H0: μ1 - μ2 = 0 What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen mode.)HA: μ1 - μ2            Based on these hypotheses, find the following. Round answers to 4 decimal places. Test Statistic =  p-value =  The p-value is     The correct…