A company that makes cola drinks states that the mean caffeine content per​ 12-ounce bottle of cola is 50 milligrams. You want to test this claim. During your​ tests, you find that a random sample of thirty​ 12-ounce bottles of cola has a mean caffeine content of 52.4 milligrams. Assume the population is normally distributed and the population standard deviation is 7.4 milligrams. At α=0.10​, can you reject the​ company's claim? Complete parts​ (a) through​ (e).       ​(a) Identify H0 and Ha. Choose the correct answer below.     A. H0​: μ=50 Ha​: μ≠50 Your answer is correct.   B. H0​: μ≠50 Ha​: μ=50   C. H0​: μ≥52.4 Ha​: μ<52.4   D. H0​: μ≥50 Ha​: μ<50   E. H0​: μ≠52.4 Ha​: μ=52.4   F. H0​: μ=52.4 Ha​: μ≠52.4 ​(b) Find the critical​ value(s). Select the correct choice below and fill in the answer box within your choice.   ​(Round to two decimal places as​ needed.)   A. The critical values are ±enter your response here.   B. The critical value is enter your response here.

A​ person's body mass index​ (BMI) is computed by dividing the weight​ (kg) by the square of height​ (m). The accompanying table contains the BMI statistics for random samples of males and females. Assume that the two samples are independent simple random samples selected from normally distributed​populations, and do not assume that the population standard deviations are equal. Let population 1 be females.   Female​ BMI: n=69 x=29.14 s=7.41 Male​ BMI: n=79 x=28.18 s=5.24   The test statistic is   The​ P-value is     Construct a confidence interval appropriate for testing the claim in part​ (a).   The ___​% confidence interval estimate is ___<μ1−μ2<___.

Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (1) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x=| S= (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ο Hg: μ= 4.64; H1: μ 4.64 Ο Ηρ: μ> 4.64; H1: μ = 4.64 Ho: u = 4.64; H1: u * 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O…

The level of calcium in the blood of healthy young adults follows a normal distribution with mean u = 10 milligrams per deciliter and standard deviation s = 0.4.  A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care.  The sample mean of these 100 measurements is  X = 9.8.  Is this evidence that the mean calcium level in the population from which these women come is less than 10?  To answer this question, we perform the following hypothesis test: H0: u = 10, Ha: u < 10. What is the test statistic? (use two decimal places in your answer) What is the p-value equal to? At the 10% significance level, do you accept or reject the null hypothesis? Answer ACCEPT or REJECT t the 5% significance level, do you accept or reject the null hypothesis? Answer ACCEPT or REJECT

A distribution with a mean of μ =41 and a standard deviation of σ = 4 is transformed into a standardized distribution with μ=100 and σ= 20. Find the new, standardized score for each of the following values from the original population. 1.Original X= 39. Transformed X=? 2.Original X=36 . Transformed X=? 3.Original X=45. Transformed X=? 4.Original X=50. Transformed X=?

For all parts of this problem, assume that the weights of tomatoes are normally distributed with a mean of 1.8 lbs and a standard deviation of 0.47 lbs.

For a population with a population mean = 60 and a population standard deviation = 9, find the score (X value) that corresponds to each of the following z - scores. A. z-= -1.00 B. z- =+0.70

Let ex be a random variable that represents the hemoglobin count (HC) in human blood (measured in grams per milliliter). In healthy adult females, x has a approximately normal distribution with a population mean of 14.0 and population standard deviation equal 2.3. Suppose a female patient had 10 blood test over the past year , and the sample mean HC was determined to be 15.3. With a level of significance a= 0.05, determine whether the patient's HC is higher than the population averages. Specifically do the following: write the data state null hypothesis H0 and the alternate hypothesis H1

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 88 and standard deviation σ = 21. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60(b) x is less than 110(c) x is between 60 and 110(d) x is greater than 140 (borderline diabetes starts at 140)

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.2.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with sample standard deviation s = 3.3. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.   (a) What is the level of significance?   State the null hypothesis  H0  and the alternate hypothesis  H1 . H0 : μ  ---Select--- ≤ < > ≠  ≥ =  H1 : μ  ---Select--- ≥ < >  ≤ = ≠    (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is unknown.     The Student's t,…