A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 40 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 41.8 milligrams. Assume the population is normally distributed and the population standard deviation is 7.5 milligrams. At α = 0.05, can you reject the company's claim? Complete parts (a) through (e). (a) Identify Ho and H₂. Choose the correct answer below. A. Ho: μ = 40 Ha: μ#40 C. Ho: μ#40 Ha: μ = 40 E. Ho: μ = 41.8 Ha: μ#41.8 B. Ho: μ ≥41.8 Ha: μ<41.8 D. Ho: μ#41.8 Ha: μ=41.8 F. Ho: μ ≥40 Ha: μ<40 (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 ± B. The critical value is

The life of a butterfly is normally distributed with a mean of 50 days. You took a random sample of 25 such butterflies. The mean life for this sample is 47 days a standard deviation of 3 days. At α = 0.05. a. Test to see if the average life of a butterfly is different from 50 days. b. Your friend believes that the life of a butterfly is less than 50 days. Is she correct?

Erin is a nutritionist and cardiologist. She is testing whether the average total cholesterol level of adults in the region is less than 175mgdL. Erin randomly selects 25 people in the region who willingly allowed their blood to be drawn for the survey. Based on several previous studies, Erin assumes that the population standard deviation for the total cholesterol level is 30.22mgdL. For this test: H0:μ=175; Ha:μ<175, which is a left-tailed test. The test results are: z0=−1.158, p-value is = 0.123   Using a 5% level of significance, which of the following are appropriate conclusions for this hypothesis test?  Select all that apply. Select all that apply: We reject H0.   We fail to reject H0.   At the 5% significance level, the data provide sufficient evidence to conclude that the average total cholesterol level of adults in the region is less than 175mgdL.   At the 5% significance level, the data do not provide sufficient evidence to conclude that…

Let x be a random variable that represents the pH of arterial plasma (l.e., acidity of the blood). For healthy adults, the mean of the x distribution is = 7.4.t A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.8 with sample standard deviations = 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 USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Hg: u + 7.4; H,: = 7.4 O Hg: H = 7.4; H,: H > 7.4 O H,: H = 7.4; H,i 7.4; H,: H = 7.4 O H: = 7.4; H,: H# 7.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large a is known. O The standard normal, since the sample size is large and a is known. O The standard normal,…

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<___.

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 μμ = 85 and standard deviation σσ = 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 125 (borderline diabetes starts at 125)

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

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.

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)