Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 18 15 19 13 11 15 18 15 12 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) (ii) Does this information indicate that the population average HC for this patient is higher than 14? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. O Họ: H = 14; H1: µ < 14 O Ho: H > 14; H1: µ = 14 O Ho: H < 14; H:4 = 14 O Họ: H = 14; H1:µ > 14 O Họ: H = 14; H1:µ # 14 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution and o is known. O The Student's t, since we assume that x has a normal distribution and o is unknown. O The Student's t, since we assume that x has a normal distribution and o is known. O The standard normal, since we assume that x has a normal distribution and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find the P-value. (Round your answer to four decimal places.)

1. Tim Hortons wanted to estimate the difference in the mean amounts of caffeine in two brands of coffee. They took a sample of 18-lbs jars of Brand I and another sample of 13-lbs jars of Brand II coffee. The following summary data (sample statistics) are collected? nį = 10 x, = 23 S1 = 3 Brand I Brand II n2 = 12 x2 = 25 S2 = 4 Assume that the two populations are normally distributed. A. Test at 5 % level of significance, whether there is a difference in the mean amounts of caffeine between the 2 brands of coffee. B. Construct a 95% Confidence Interval to estimate the difference in the mean amounts of caffeine in 2 brands of coffee. C. Does the result in part b) confirm your findings from part a)?

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.

The random variable Z has mean 30 and variance 225. Calculate the limits between which you would expect the bulk of observations to lie for the random variable Z/3 − 7.

There are two independent random variables X and Y. X has mean 4 and standard deviation , and Y also has mean 4 and standard deviation . A random variable W is the difference between X and Y. That is, W = X - Y. Calculate the mean of W.

An experiment where a patient's blood pressure is measured before a treatment (call it X;) and after the treatment (call it Y;). The difference in the blood pressue of each patient, Z; = Y; – X; is also recorded. The sample size n of patients is large. Suppose the true population mean of the patient's blood pressure before treatment is 41 and after treatment is 42, both unknown. Suppose the true population variance of the patient's blood pressue before and after treatment are the same, but unknown. Find an approximate 1-a confidence interval for 12 - 41- 2.