A random sample X₁, X2, ..., X10 is drawn from a normal distribution with variance 12. Let X be the sample mean. Let x², be the 100pth percentile of a chi-squared random variable with v degrees of freedom. The following table lists values of x², for specific combinations of p and v: v = 8 v=9 A B с D p= 0.5 p=0.6 8.351 E 7.344 Find the probability that Σ;", (Xi - 8.343 Less than 0.3 9.414 P=0.7 9.524 10.656 At least 0.3, but less than 0.4 At least 0.6 At least 0.4, but less than 0.5 At least 0.5, but less than 0.6 x)² i is greater than 120.

Determine the appropriate z or t alpha value and calculate the error bound for the mean.

One property of the F-distribution used for the Analysis of Variance is thatA. It is symmetric.B. The exact shape of the F-distribution depends on two different degrees of freedom.C. Values of the F-distribution can be negative.D. The total area under the curve is equal to 2.

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.