Researchers studying the effects of diet on growth would like to know if a vegetarian diet affects the height of a child. The researchers randomly selected 12 vegetarian children that are six years old. The average height of the children is 42.5 inches with a standard deviation of 3.8 inches. The average height for all six year old children is 45.75 inches. Conduct a hypothesis test to determine whether there is overwhelming evidence at α = 0.05 that six year old vegetarian children are not the same height as other six year old children. Assume that the heights of six year old vegetarian children are approximately normally distributed.

A clinical researcher performs a clinical trial on 12 patients to determine whether a drug treatment has an effect on serum glucose. The sample mean glucose of the patients before and after the treatment are summarized in the following table. The sample standard deviation of the differences was 6.   Sample mean glucose (mg/dL) Before treatment 114 After treatment 108 What type of hypothesis test should be performed?Select: Left-tailed z-test Unpaired t-test Two-tailed z-test Paired t-test    What is the test statistic?   What is the number of degrees of freedom?   Does sufficient evidence exist to support the claim that the drug treatment has an effect on serum glucose at the α=0.05 significance level? Select: _____Yes  OR  _____No

Dr. Graham is interested in determining if middle-aged adults use text messaging more or less frequently than the general population. Dr. Graham collects information on text messaging from a random sample of 50 adults ages 25 to 44. Dr. Graham finds that these individuals send or receive an average of 68 text messages per day. Using the population mean (and standard deviation) of 41.5 texts per day (34 texts per day), determine whether adults in this age group use text messaging more than the general public.

In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 3030 scores from all of the students who took the test. She sees that the mean score is 169169 with a standard deviation of 7.06747.0674. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 1313. Is there evidence that the standard deviation of test scores has decreased at the α=0.005α=0.005 level? Assume the population is normally distributed. Step 1 of 5:  State the null and alternative hypotheses. Round to four decimal places when necessary. Step 2 of 5:  Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.     Step 3 of 5:  Determine the value of the test statistic. Round your answer to three decimal places. Step 4 of 5:  Make the…

A Two-Sample Hypothesis TestThe mean number of English courses taken in a two-year time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of three English courses with a standard deviation of 0.8. The females took an average of four English courses with a standard deviation of 1.0. Are the means statistically the same? (Assume a 5% level of significance.)Useful tools:Normal Distribution Calculatort-Distribution Calculator 1. Which of the following null and alternative hypotheses match this scenario? A---H0:Δμ=0H0:Δμ=0Ha:Δμ≠0Ha:Δμ≠0 B---H0:Δμ≠0H0:Δμ≠0Ha:Δμ=0Ha:Δμ=0 C---H0:Δμ=0H0:Δμ=0Ha:Δμ>0 2. Which type of test should be applied? A---The alternative hypothesis indicates a right-tailed test. B---The alternative hypothesis indicates a left-tailed test. C---The alternative hypothesis indicates a two-tailed test. 3. Which type of distribution should be…

Do political science classes require the same amount of writing as history classes? The 47 randomly selected political science classes assigned an average of 14.5 pages of essay writing for the course. The standard deviation for these 47 classes was 4 pages. The 41 randomly selected history classes assigned an average of 16.7 pages of essay writing for the course. The standard deviation for these 41 classes was 3.6 pages. What can be concluded at the αα = 0.01 level of significance? For this study, we should use        The null and alternative hypotheses would be:        H0:H0:     Correct      Correct    Correct       H1:H1:     Correct      Correct    Correct The test statistic     =  (please show your answer to 3 decimal places.) The p-value =  (Please show your answer to 4 decimal places.) The p-value is     αα Based on this, we should      the null hypothesis. Thus, the final conclusion is that ... The results are statistically significant at αα = 0.01, so there is sufficient…

In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject. The study revealed that the overall physical activity of obese young adults has a mean of μ = 325 cpm and a standard deviation of a = 90 cpm. In a random sample of n = 100 obese young adults, consider the sample mean counts per minute, x. Click the icon to view the table of normal curve areas. a. Describe the sampling distribution of x. Find μ. Find o-. X 0-= (Type an integer or a decimal.) Describe the shape of the sampling distribution of x. ✩ OA. Skewed right OB. Approximately normal OC. Skewed left b. What is the probability that the mean overall physical activity level of the sample is between 300 and 310 cpm? P(300 ≤x≤310) = (Round to four decimal places as needed.) c. What is the probability that the mean overall physical…